The beauty is that you just need to hit $6 once and then don't really need any money until you can consistently draw your whole deck.
Which is nice, since focusing on engine building would let you play Altar more.
So what helps get you an early $6? Here are the major contenders I can think of (I'm sure others can think of many more).
- Baron looks fantastic. Use your engine to help connect Baron to Estates later even if you start trashing them. It's probably often easy to build an engine that can overdraw to re-discard the same Estate repeatedly. Late-game Altars can gain you your payload as well as your engine if necessary, and Baron's +Buy can provide Coppers to trash with Altar if you run low.
- Quarry looks strong too. If you want to prioritize engine building over an economy then you might really need some help hitting $5, especially on Altar turns. Yeah it can't buy Gold but it's an Altar game: most likely you have good Actions you're happy to buy? Later you can trash the Quarry to Altar if you want.
- Mining Village looks plausible enough. It can be an engine piece, and you probably won't feel as bad about trashing your first one to buy the Altar as you would in a game with less card gain. These decks really want to end the game in a big flurry of Duchy gains and Mining Village trashing which will leave the deck in shambles; I'll leave it to better players to decide whether this is a positive or a negative.
- Count and Death Cart look good. Again, these decks will implode pretty quickly on command (especially Death Cart).
- Mandarin is an interesting question. It slows your opening down when Altar needs speed. On the other hand it would enjoy an engine game, and if you want Altar it's likely because there's something else interesting at $5 which you might happily buy on turn 2 after Mandarin.
- Cache and even Beggar are intriguing but probably not worth it. I don't place a lot of stock in Altar deck thinning even if you do manage to grab Altar on the first reshuffle, so these would really hurt. Although once you have Altar to take care of the serious deck building I imagine you safely can, and probably should anyway, spend a turn to buy Spice Merchant or Loan or Warehouse; perhaps the problem could be controlled this way.
- Contraband looks decent. Very likely you can take Gold if Altar gets blocked; and on a good Altar board there's likely something good at $5 if you don't hit $6. Later you can trash the Contraband. But I always want Contraband to be good, so I'm biased.
- Vault of course is absolutely reliable for hitting $6 and can work well with engines. But Vault might just compete with Altar, especially without +Action: do you need two different cards that give reliable $5 turns?
- Merchant Ship and Wharf are pretty decent I guess? Both good BM enablers so you have to watch out for that, but also sometimes you would like to have lots of them.
On the flip side, Altar seems to be rather in competition with a card like Horse Traders, which provides a legitimate alternate road to $5 hands but doesn't really help hit $6. I can't think of many other cards that help you hit $5 but not $6 (well, Feast and University) but I'm sure they exist. Obviously Altar also tends to compete with strategies that don't involve building a strong conventional early economy at all: Chapel, Potion, etc.
I think the most effective use of Altar is to use it gain your big $5 engine piece while spending your small amount of coins on the $3-4 piece until you can consistently draw your deck and play the Altar every turn.
Based on this, a few other combo ideas occur. Menagerie will love Altar's deck thinning, ability to gain lots of variety, and maybe even its handsize reduction. Of course lots of cheap good engine pieces are good here: Hamlet, FV, Watchtower, Squire (which could also be trashed into an Attack by Altar). But even typically weaker ones (Courtyard, Moat, Shanty) can be strong when paired with a plentiful power $5; and a $2 price point might be a perk while your economy is weak.
At least one Scheme is probably a must-buy. At minimum, if it gets you even one extra Altar play in the phase while you're setting the engine up, then you'll make up for the buy you spent on the Scheme so it's basically free. But beyond that, Scheme provides an alternative way to play the Altar every turn without getting an engine running quickly. This would, I imagine, let you use the Altar for some engine-incompatible plans (e.g. Dukes), or plans that just don't get your engine humming very quickly (City engines, and maybe some other super strong all-$5 engines where the payload is the only cheap card involved). Note also that an extra, permanently topdecked Scheme can be used as guaranteed Altar food, if that's worthwhile to you.
Altar robably goes well with Double Tactician under the right circumstances too. It probably gets rolling about as fast as most other Double Tac decks, since they all have to get a good payload assembled and buy two Tacticians. And once it starts you need very little or no more card draw because you're trashing almost as fast as you gain; so unless you're getting attacked your deck size will stay pretty close to what Tactician can handle.
It could maybe work well with Hermit/Madman: it's undoubtedly a great excuse to skip buys. Might help if your favorite $5 card gives +Actions to play both Altar and Hermit in the same turn?