I don't usually comment on lists as it's is very much a personal preferences game, but here are a few thoughts anyway:
1) Tacticals without mobility are dead/useless tacticals. You want to get them into shooting range to be effective. I strongly urge you to go with at least rhinos. You can get the unit to objectives (usually), park on them, and fire away with your plasma weapons. Rhinos are a bargain.
2) Vanguards are not worth the points IMHO as they are usually a suicide squad. They are very much hit/miss, and mine have failed more than they've succeeded. I prefer Ironclads in Lucius drop pods for assaulting the enemy backfield (although they are elite not fast attack). If you must have an FA unit, I'd use a storm with HF and 5 CC scouts & combi-melta/flamer & PF on the sarge. Not as powerful as VV's, but still tie up other units nicely, and more versatile (i.e. can reserve for late game objective pounce if needed). Ditto for assault squads, and they're even less effective than VV's. I'd use speeders over assault if I had to make a FA slot choice.
3) HQ. Fine if going with assault unit. If not, I think Vulkan or librarian with TA/SS with termies would be better (of course one less termie to fit in LRC).
4) For Sternguard, I like to play them with all combi-meltas (if 5); or 5 combi-meltas, 5-combi-flamers (if 10) in a pod. Definite vehicle killer, and the latter (due to combat squadding) then roasts the unit inside if a transport.
Love your HS choices, play these three the most myself. The TFC is the most under-rated, under-played unit in my LGW. Love it. In a fortified ruin it can last a long time with that 3+ cover save if not assaulted.
