I agree. TASM is hard to find on the net, no longer maintained, doesn't support 64-bit, has a lot of useless assembler directives and a few annoying bugs and there's no source available to fix it, so I'd keep away from it. I can't say much about HLA, I've never used it and I don't know anyone that does, but I've heard good and bad about it.
About 64-bit development, 64-bit programs tend to run slightly faster (if done properly) thanks to the additional registers and larger register size. Also, more than 4 GB of memory can be addressed directly if needed. Although 32-bit programs will run under a 64-bit environment as well, so it's not strictly necessary to move to 64-bit in the near future.
I've found MASM32 to be the best for doing larger Windows programs. It doesn't support 64-bit, but it's actively maintained and has very good macros and options for Windows development. However, you'd still typically use C to do larger projects anyway.
FASM and NASM can do pretty much anything you need. Both can do 64-bit, are actively maintained/developed, they have simple and logical directives and Linux ports are available. All assemblers have slight differences in syntax, but most still use the standard Intel style.
For learning asm I'd suggest The Art of Assembly
by Randall Hyde.