All LS motors are compatable with each other mostly. Depending on the crankshaft's reluctor ring (24 or 58 tooth) will dictate which PCM it'll take to control it. Earlier stuff is 24 and around 2005 things switched to 58. There are some other little differences, knock sensor location, cam sensor location, but all can be set up to work. Of course if you put a carb on it none of this matters. Physically the biggest difference between blocks is bore size and to run the rectangle port heads (L92, LS3, L76, ect) you need a 4" or bigger bore. You run into differences in valvetrain and intakes if you use the newer style heads. The older cathedral style heads (LS1, LS2, LS6, LQ9, LQ4, most 5.3, ect) work well and are easier to get, but there are benefits either way.
Depending on power goals and budget there are many ways to go. 5.3s can be had in the junkyards cheap, from pan to intake for around $500, the LS1 style computer which was used in all the trucks, Vettes, f-bodies is cheap as hell and is still a really good tuning platform, needs to be 24 tooth reluctor and a 1x cam signal. Spend a little more money and go 6.0L with an LQ4 or LQ9, these blocks are identical, the only difference is the LQ9 uses higher compression pistons, so if you're going to rebuild don't waste the extra money on the LQ9. It costs more because its rare, they only put it in a few trucks mostly Escalades. With the LQ motors you can run the newer style heads if you want, but if you get a complete motor the 6.0L heads are really good for stock heads, they share the same ports as an LS6 head with bigger chambers.
Point is there are tons of good options, and you are only limited by your budget.
I personally think that the best bang for the buck is a 5.3 complete, swap an LS1 intake and stuff on, and spray the guts out of it. This in a lightweight car would go 10s, would easily go 11s in a Camaro.
The way I went was a LQ4 with forged rods and pistons, LS1 heads, cam and bolt-ons, I've got around $4500 in the engine with machine work, gaskets, and everything. I wouldn't bat an eye to push over 700 wheel with mine. If I put "good" heads on it, it should pick up a lot more, but I'm cheap.
You could take a cheap 5.3, overbore it to LS1 specs, and pick up lots of used parts cheap, and spray the house down. Honestly iron block are whats going to be affordable, everyone wants too much for anything aluminum, and iron is only about 100 pounds heavier.