What ships are needed to run high sec combat sites? From what I have read, it seems that it varies from frigates to cruisers, with the HAC being the preferred option for most combat sites. Wormhole sites I assume are T3 cruiser territory.
for whs you assume wrong. Read about whs, there are different types of whs, from c1 to c6. For c6 you need capitals, for c3s probably bs or t3cs, etc.
All green sites (anomalies) in HS can be run in a properly fitted and flown T1 frigate.
Combat signatures that you have to scan down or expeditions/escalations vary by the difficulty: some are gated and only certain types of ships can enter, others can be done in anything but generally 4/10 DED-rated sites or unrated of similar difficulty should be done in cruisers+.
There are different difficulty classes of wormholes, as a general rule of thumb:
C1 - T1 cruiser
C2 - T1 battlecruiser or T2/pirate/T3 cruiser
C3 - T1 Battleship
C4 - Multiple BS or a single pirate/T2 BS
C5 - Multiple pirate BS (rattlesnakes, nestors or leshaks usually)
C6 - Capitals + support
If you want to run sleeper data/relic sites, move up a difficulty class. (C2 relics are roughly as difficult as C3 anoms.)
Wherever I say T1 you can also use a T2/pirate/T3 of a lower size (for example, a worm or assault frig can easily run C1 anoms.)
T3 cruisers aren’t very useful for a lot of WH PVE (they are very popular in WH PVP though.)