For the purposes of this discussion I will reference this.
To start off, I feel that it isn't worth worrying about having Pokemon specifically to counter Tier 1 and Tier 2 raids. I have solo'd all the tier 2 raids with just Dragonite/Gyarados, any high CP attackers. It wasn't even close, so it feels like you should look to optimize tier 3/tier 4 raids to have the better chance of completing them with fewer people.
Looking at the pokebattler chart that I linked, we should look at what Pokemon appear multiple times as a top counter and prioritize them; this would reasonably be the most efficient way to power up Pokemon.
TOP PRIORITY POKEMON:
1. MACHAMP with Counter/DP, then Counter CC
Machamp is top priority based off it having the (second) most appearances in top 3 counters; and they happen to be on the most sought after mons on the lost. Lapras, Snorlax, and Tyranitar and eventually Blissey all have Machamp as #1.
2. RHYDON with Mudslap/Earthquake or GOLEM with Mudslap/Earthquake
Golem appears the most on the list; four times actually. However, one of those times is vs Charizard, and this is the only time when Golem with double rock moves appears on the list. The other three times are all double ground. This means that one Golem or Rhydon is a top counter to multiple raid Pokemon; specifically Arcanine, Jolteon, and Flareon. On the list linked at the start of my post, Golem appears above Rhydon, although I am unsure as to why. When I ran the tests on Pokebattler myself, Rhydon appears to be slightly more favorable than Golem. Either will work in this case, whichever you happen to have; they both perform the same function with Rhydon doing it slightly better from what I can tell.
3. TYRANITAR with bite/crunch, possibly Bite/Stone Edge
Tyranitar is by far the best dark type in the game, this makes it the best counter to Gengar/Alakazam. Gengar and Alakazam are also generally highly sought after Pokemon; probably after what Machamp handles (Snorlax, Lapras, and Tyranitar). For some people Tyranitar may be a higher priority than Golem/Rhydon simply because of Alakazam/Gengar being (generally) more sought after than the more common Arcanine, Jolteon and Flareon. *** Tyranitar can also be used with Bite/Stone Edge, however this lowers its effectiveness against the previously mentioned Pokemon, but allows him to take care of Charizard and Flareon as well.
4. DRAGONITE with Dragon Tail/Outrage or Dragon Tail/Hurricane
Dragonite is next on the list mostly because of it appearing as a top counter to both Machamp and Gengar. Gengar is indeed already covered by having TTar, but the top counter for Alakazam appears only one time as a top counter. This means that if someone was trying to be as efficient as possible, they could get a Dnite to cover two raid Pokemon if they didn't have Ttar; rather than having just Alakazam to deal with Machamp. Most of the other top raid Pokemon have top counters consisting of Pokemon that appear only once. In these cases the most efficient thing to do would be to reuse top attackers from other raid Pokemon; for example, Dragonite is a strong general attacker, as is Gengar and Alakazam. It is also worth nothing that if you don't have Machamp, you will definitely be wanting one; and Dragonite can help you get there.
Another option is to use generic type-based counters. For example:
- Venusaur: Flareon
- Charizard: Vaporeon
- Blastoise: Jolteon
- Rhydon: Vaporeon
All very common, generic, easy-to-get Pokemon.