An LSx FD can be daily driven, but it should be incredibly well sorted.
Most ls1fd's for sale do not have A/C. Some do not have a/c or Powersteering (looped hydraulic rack... very few have the Maval rack true manuel conversion).
I know this is not a problem on a weekend car, but lets be honest... you want a daily driver. I daily'ed mine for a few months and it was great fun, but the concerns of door-dings, theft, and not having a/c, really started to make me miss having a DD that I didn't really give a crap about.
Again, my vote is C5 vette, as it is factory well-sorted. You know what you're getting. You can find a wiring diagram if something goes wrong, and track down the issues. No mixing and matching of manufacturers(Chevy motor, Mazda Body, Ford rear, custom mounting equipment, and a possible hack-job wiring), reduces the number of headaches for something that is supposed to be deadnuts reliable.
I'd go I/C/E and some decent suspension. Don't worry about the heads.

cam = 200ish
Long Tubes = 1000-1200ish
LS6 intake = 300ish
CAI = 200ish(?not sure as FD's don't use this type)
Ported 5.3L factory heads around 1500ish, but when you have it open, you'll want to also replace lifters for 200ish, and pushrods for 200ish, and rockers for $350ish