Hello, long time vCoH veteran here. I'll answer your Qs.
I've been trying to pick up CoH1.
However, one thing that's vexxing me is that it is extremely difficult to predict how unit X performs against unit Y, until I've tried that combination.
For instance; are Rangers any good at all? If so against which units, and when (if ever) do you upgrade thompsons?
Rangers due to their high initial cost and high reinforcement cost are limited to a support role. At most 2 would ever be purchased in a real game, but this is very unlikely. They are most often called in when the USA player does an infantry heavy upgrade opening (BARS+Nades for example), and does not inflict enough early game damage, and thus has no fielded AT weapons when a puma hits.
Rangers are almost always upgraded with Thompsons, since their anti-infantry capability with it is good (can easily 1v1 any german squad that's not vet3 or has MP40/MP44), and since their anti-infantry capabilities without it is very poor.
Keep in mind though, if you are getting rangers, that they are mostly considered a "panic" unit (panic rangers vs puma suprrise). Bazookas in CoH1 are quite different than in CoH2 in 2 ways: much less penetration (meaning they are completely ineffective against tank front armour for the most part), and less accuracy. Use them only to support infantry vs light vehicles or tanks that you can flank.
Which units deal damage most reliably vs 251 half-track and the Puma?
If your strategy is a fast M8, that should be enough to force any 251 or Puma to play defensively. The best counter for 251/Puma is either: AT gun, M10/Hellcat, or a mine (mines do 200% damage vs these light vehicles, and will destroy the engine) in combination with sticky, AT gun, M8, or tank.
If I want to avoid using snipers, which weapons do I use vs Vet2 Grenadiers? Is this the same for Vet2 Volks?
Snipers are always the best bet vs. VET2 Grenadiers since they have a 300% accuracy modifier against them (AKA, will always hit them on retreat), and VET2 gives Grenadiers "Elite Armour" (-25% received accuracy). However, vetted riflemen perform well against all axis infantry, and flamethrowers do bonus damage vs VET2 Grenadiers. The M8 can also be a reasonable choice, and of course the Sherman. Off map howitzer barrages also have a tendency to 1 shot Grenadier squads that are capturing, and is a good way to eliminate squads from opponents who aren't paying attention.
The Volksgrenadiers do not receive Elite armour at Vet2, and just receive -25% received suppression, and -5% received damage. BAR rifles, flamers, and any vehicles should fare well.
Which units are bazookas good against; are they better than recoilless rifles at anything?
Bazookas are good against tank rear/side armour, and puma/251 vehicles, but have poor accuracy in general. Recoilless rifles have better accuracy and penetration, so are better against all tanks than bazookas, and due to a weird "phasing bug", they tend to travel through pumas/251 quite often, and thus have poor accuracy against these units. In general, bazooka good vs light vehicles, bad vs armour, and recoilless are the opposite.
If somebody has a link to something that describes the target-tables in play here, I would appreciate it.
Thanks.
Use this websites for detailed stats:
http://hq-coh.com/stats/coh-stats.com/Main_Page.html
Extreme detail on target types:
http://companyofheroes.wikia.com/wiki/Infantry_Type
Note: that it might look confusing, but it isn't too bad. For example, all small arms except snipers are .85 acc and .75 dmg vs heroic armour.