You are not getting a Huracan worth owning at your price point as previously noted. I always felt the Huracan looked "fat" personally and I am not a fan of the pressed carbon fibre look.
Gallardos are great cars. I had one for ten years and all it basically required was maintenance and tires. I would look for a 6 speed manual as the e gear is clunky and the clutch wear is significantly greater regardless how carefully you shift. Also a pump can fail on the e gear and I believe it is close to a 5 figure repair. In 2006, the HP was bumped slightly and the gearing shortened among other improvements. I think the 06 and up are better built, doors feel heavier, and anecdotally knowing owners of 04 and 05 cars, my 06 seemed a lot more reliable.
As you will be purchasing a 12 - 13 year old car, you are going to start to experience wear and tear failures like water pumps, alternators, belts, and hoses. So you should budget accordingly. A lot of the parts are of AUDI/VW origin so shop around. Even though you are only paying $125k now, you will be maintaining a car that cost $225k to $250k when new.
I would avoid super low mileage cars, you'll pay a premium and since they haven't been exercised regularly they are probably in worse condition than less expensive medium mileage cars with a full service and maintenance history at a dealer or reputable aftermarket shop.
Colours - Black, yellow, green and orange will command a premium over other colours.
I would avoid the convertible, a lot more expensive parts and systems to fail. Also, you can't get a glass rear bonnet and you lose a really useful storage space behind the seats if you want to go on road trips with your significant other.
Another option to consider would be an R8, my buddy picked up a pristine 25,000 mile 08 V8 6 speed for $70k, a couple of years ago. The R8 v10's are cheaper than corresponding year Lamborghini. R8's IMO have better interiors and more headroom too. Obviously service options are far greater for Audi than Lamborghini as well.
You should do as extensive test drive as possible. Drive a few to get a sense of what a good one feels like.
Mid engine exotics aren't for everybody. They are loud and uncomfortable with awful visibility. They also attractive a tremendous amount of attention from the general public (male) and LE which is not for everybody.
You should also factor in insurance costs and if you don't have an umbrella policy, get one. If you get into a serious accident whether it's your fault or not, you are probably going to be sued.
If you find a car, post it here. Somebody will probably know if it was any stories. Also you can get feedback on pricing, condition here as well etc.