I’m by no means an expert at Codex, but I have a lot of experience with similar games such as Magic and HS and I think a discussion about Player 1 and Player 2 roles would be useful. These are more general strategies/advice, but the most important concept is to think about how your role will affect the game. If you are playing Mono-Red vs Mono-Red for example, it’s a completely different strategy whether you are P1 or P2.
Your role is the aggressor. You dictate the pace that your opponent can play the game.
First you have a major economic disadvantage. Over the course of the first 5 turns you will have at least 5 less gold than your opponent. This is a real downside and means your gold should be spent as optimally as possible to create good trades and apply pressure. Additionally your opponent will be on the defensive and can utilize the patrol zone bonuses better than you can. This means you could be farther behind on gold if they use Scavenger or they could be use more cards with Technician. Finally you’ll have to punch through a point of armor when they want to defend their heroes/tech buildings instead of getting resources thanks to Squad Leader.
Second your opponent will have the first opportunity to build Tech II buildings and therefore play advanced tech II units. This means while you get to attack first you will have some turns where your units are being outclassed - your tech I vs their tech II. This disadvantage is reliant on some variance - even if they tech in those units, they may not draw them on their cycle. Also if you can pressure them into going down to a 3 or 4-card hand and then deny them the technician bonus, you’ll make it more difficult for them to draw their tech. Ultimately the worst thing you can do is play too safe. If you play passively as P1 you are inviting P2 to turtle and tech up and this can lead to a lot of bad scenarios if you aren’t able to break their tech buildings.
While those are big disadvantages, your Player 1 advantage is enormous! You are the first to act and will always get to set up advantageous attacks in the early game (outside of haste from your opponent). This means you will have a much bigger advantage by playing your hero Turn 1 because you get to attack with that hero first. If you can kill an opposing hero, you can recoup some of that gold deficit. Simply playing your hero could deter Player 2 from using a hero. That means you also shut off every spell in their starter deck! You also severely limit their early tech options; if they are too timid to summon a hero then they aren’t teching in spells for their heroes.
The first big push for Tech I units is available to P1. Since neither player can tech on the first turn, even though P2 can build a Tech I building first, P1 gets to draw and deploy their Tech I units first. This advantage should be used to try and get a hero kill or to weaken their board without losing too much of your own. Pressing this advantage is not always possible due to variance - sometimes you will not draw your tech I units and then you will have a difficult time pressuring your opponent. At this point you may have to try a subpar strategy like dumping all your gold into a durable hero (not against white or purple starter or against Necromancy) or building a tower/surplus.
There is also a ‘Hero Shove’ tactic that works well as P1. Basically you dump a lot of gold into a hero and mid or max them early (T2 or T3), hopefully to some large-board sweeping effect or some long-term benefit. You get to tech in the hero’s ultimate (rather than tech I units) and threaten to use it early. This strategy can be used with a variety of heroes (even ones without good ultimate spells, like Zane). It’s important not to fall too far behind on your economy when you do this because now P2 has more incentive to drag the game out and while you’ve been investing in your hero, they have probably been investing in tech buildings and tech I units.
One of the biggest mistakes you can make as Player 1 is being too passive. Since your opponent will inherently have a gold advantage and they will be able to build and deploy higher tech II units before you, the clock is ticking for you to win or pressure them so much that it is difficult for them to tech up on time. Also it is generally better to attack and trade units. If you let them have a small deck because you are both assembling armies, that makes it easier for them to draw into their better tech faster. Attacking and trading units gives them less options for attacking back, but keep in mind the bonuses you’re giving them. You don’t win the game by having a lot of gold or cards, but getting too far behind can prevent you from winning.
Tl;dr The amount of pressure Player 1 uses will literally dictate the pace of the early-mid game and what options Player 2 has.
Your role is the reactor. Your reactions to your opponent’s strategy will determine whether you win or lose.
Player 2 is on the defensive from as early as Turn 1. Some cards and tech units are aggressive and become worse as Player 2 and it’s important to properly evaluate them. For example in Necromancy you have Bone Collector and Hooded Executioner as your Tech I options. These two do a great job highlighting the difference between P1 and P2. Bone Collector has a trigger that works on attacking which indicates it’s a good tech I unit for P1. If you never get to attack with it, the utility of having a Hooded Executioner may be more useful in the later game. Of course Bone Collector’s threat of attacking can force your opponent to spend more resources than they planned to kill it, which is value in and of itself. Hooded Executioner’s boost ability requires a significant gold invesment that can be difficult to pull off early game as P1, but not as difficult as P2. As P1 if you play a Hooded Executioner without boosting you aren’t getting a terrible unit, but generally you could have got a better unit in Bone Collector (at least for the early game). The lines between a good unit for P1 or P2 are not always so stark, but you should take care to think about what the unit will be doing (attacking or defending) when you tech it.
Keep in mind that P1 will get to tech and play Tech I units before you and try and guess which units will be coming in for them. If you can tech cards that match up well then that will translate into a board advantage at some point. For example if you are against an opponent who has good 2 gold 3/3s (like Necromancy), try finding 3/4s you can use.
You do have some strong things to take advantage of as P2. With your increased gold you can match your opponent’s spending on heroes/units and build a Tower for free! However that is not always the best play. Towers are good against aggressive P1 opponents who are attacking frequently with small units. It’s also a great play for the Detector quality in certain situations. If P1 is not being aggressive then you should reconsider the Tower because you might be throwing away one of your biggest advantages as P2. Extra gold can be spent on leveling up your heroes, giving you an advantage on defense or by being disciplined about teching up. While you have a gold advantage, the fact that P1 always acts first means they start the game with 4 gold more than you, though over time you will far surpass how much gold they have spent (if you live long enough).
The tech advantage is a huge thing to be aware of and to leverage. The difference between starter units and tech I units is not so large, but instead of paying 2 gold for a 2/2 you could get a 3/3 or pay 0 gold for a 2/2. These small incremental advantages can snowball into a big lead heading into the mid-game. Since you will be teching up to tech II sooner than P1 generally, the onus is on you to decide the strategy you would like to take. Most of the time you will have to base this on the starter your opponent is using - if they have the red starter then it will be important to have high-toughness units, whereas if they have the black starter you will want cheaper units especially if you can get several units from 1 card. Take their early plays into account as well - if they are going for an early maxed hero, then there are other things they aren’t doing. You will also need to formulate a strategy to win on the back of your superior tech. It’s no good getting to tech II before your opponent and then not turning that into a strong advantage. Not all tech units are made the same. Some are better to answer an opposing strategy than to just win the game on their own.
Player 2 has much more reason to use the Patrol Zone than Player 1 and making a poor Patrol Zone can be the difference between winning and losing the early game. If you are summoning a hero as P2 then you need to protect that hero by placing lots of units in the PZ or by getting a significant value if they go after your hero and spend too many resources to kill it. The Squad Leader position is great for heroes because they will typically have to spend extra resources to get through the additional armor. Elite is great because it usually means the enemy hero has to level up before it can kill your hero, for example Vandy in Elite against Calamandra and Tiger Cub. If Vandy was in Squad leader, then it’s a fairly even gold trade (they get 2 gold for killing Vandy and invested 4 into Cal and Cub, while you invested 2 in Vandy), but in the Elite position they need to level Cal up before she kills Vandy or have some sort of bonus. Elite is also good for trading up; starter units with +1 ATK can trade with weaker tech I units sometimes. Lookout is good if you are expecting enemy spells like Origin Story or Snapback. Knowing when to go for the gold bonus of Scavenger or the card bonus of Technician makes assigning patrollers very difficult to perfect, but you will have more practice when you are P2.
Tl;dr Properly reacting to what Player 1 is doing will give you the best chance to bury them in your natural gold advantage.