Ok I'm slightly confused. Is there a reason you need a car to run TWELVES for a daily driver? You said you can't stand not having enough power to do "lane changes etc", but a car that runs 12's is a bit much I think, especially considering your budget. If you want something that is "$5k~$10k max and rest for mods." then you might as well get an old Civic hatch, toss a B18 or H22 in it, boost it, and call it a day, otherwise, I think a bone stock 350z/G35 would do you fine. Yeah a high 13/low 14 second car isn't the same as 12's, but you are talking about a daily driver here, not a race car.
The VQ35 in the Z/G is fine but they don't like boost without going with forged internals, and that costs bank. I am a mod for a 350z site and know quite a bit about them, so I am not making that part up. We have had SEVERAL members lose their boosted motors because they weren't forged, and a couple that blew up even though they were forged. The VQ is fantastic in NA form, but after that you are looking at a serious money investment if you want reliability.
My realistic suggestions for your budget would be:
Cobalt SS (preferably the turbo version)
Civic with lots of mods
Terminator (03-04) Cobra with a pulley
Camaro SS or TA WS6 with some bolt on's
I mean, if you want a 12 second car for your daily driver that you are going to put a ton of miles on, that's your business, but I honestly think you would be happy with a car that will run high 13's. Just my 2 cents.