Armour:
Mk I and II is outdated by this point. Mk II would be the standard armour if the army is poorly supplied.
Mk III would conceivably be used on assault units, but is mainly a pseudo-terminator tunnel-fighting/enclosed spaces variant of Mk II; so don't use too many.
Mk IV: Relatively common in a immediate-post-heresy army. This was the standard suit worn by the better-equipped space marines (Imperial Fists and many of the renegade legions) at the start of the heresy; though bear in mind distant or poorly equipped legions (like Raven Guard) would still have been using Mk II as standard.
Mk V: Again, relatively common. Less so than IV; it was introduced as a stop-gap, had many technical faults (not least the exposed cabling on the chest) and was notoriously difficult to repair/maintain. The Worldeaters had lots of these (presumably they didn't mind!). Leaps and bounds ahead of Mk II and variants.
Mk VI: This would be very common ? it was just being introduced as the Heresy erupted, and the second founding chapters/surviving loyalist legions would have been supplied with these as Mk IV was phased out.
Mk VII: Rare; some specialised units (command squads, veterans etc). If you want a distinctive look to your army, try no to use it at all. This is the single most identifiable 'thing' of a marine army, so you're going to have to camouflage it if you want an immediately identifiable immediate-post-heresy force.
Mk VIII: Not yet developed.
There was less standardisation in marine equipment at this point, so variants on the suits (which were modular ? Mk VI helm is compatible with anything Mk IV+, for example) would be relatively more common.
Terminators are relatively common: the technology to build them is still around. The 'modern' versions (Mk IV Terminators?) that we think of as terminators are presumably developed (the Mk V helmet was a spin-off from the terminator design); but if you want to play it safe, use the ones depicted in the Horus Heresy art books.
Tanks:
Razorback is a no-no.
Predators can only have autocannon turrets.
No Land Raider variants (you ought to check out the Forgeworld pre-heresy raider, too)
Land speeders are pretty common.
Whirlwind is okay.
Drop-pods are iffy...
Dreadnoughts definitely around: and still suits of armour rather than sarcophaguses.
Guns:
All sorts of weird combinations available:
Autocannons common (count as heavy bolters)
Conversion beamers available (but rare ? count as plasma cannons)
Since terminator armour is still in its infanct, their weapons are still catching up. Assault cannon is not available yet; nor is the cyclone missile launcher. Thunder hammers are still power maces; and Storm shields as we know them are iffy.
(You can make RT-era boltguns pretty easily by swapping the magazine section and the handgrip over on one of the new boltguns.)
Other stuff:
Arguably, Librarians would still be verboten...
Chaplains exist...
Jumppacks are around...
Scouts could be a mix of new recruits and specialised marines as the Codex changes came into effect...
As to the chapters that existed immediately post-heresy; check this entry on wikipedia:
http://en.wikipedia.org/wiki/Second_Founding
That's the official list, but you could easily make your own by using one of the unnamed Ultramarine successors.
Hope that helps!