If you are looking to do your first track day, just use whatever car suits your daily driver needs.
Most FWD cars on stock suspension will have significant body roll and understeer and eat front tires if driven very aggressively. So, don't go to your track day on brand new ecopia's that you want to get 60k miles out of. Stock or non performance brake pads are likely to overheat and fade pretty easily too.
If your are trying to plan ahead on becoming a track day enthusiast, I would stick with cars that have inexpensive ways to increase front camber and have aftermarket sway bar options and performance brake pads available to save your tires and keep your brakes solid on track.
There is a thread on here about a guy tracking a FWD impala - it's a pretty good read for what to expect from a stock, fwd platform. Sorry, couldn't find it to post.
PS - I think a P71 would actually be a pretty decent car to drive on track, but would eat brakes and tires due to weight and body roll.
Snrub
Reader
4/9/18 10:01 p.m.
If you're not thrilled about the suggestion you're getting, perhaps you can provide additional parameters. What size of car are you looking for in order for it to be "family friendly?" Everyone's definition is different. If I procreated I'd be fine with the kid having a compact sized back seat. If you want P71 size, you can get 3.5L Dodge Chargers for your price range. I have no idea if they can handle track use and I don't think they're super reliable, but I'd be more tempted by them than P71s.
Just for the record I searched for appropriately priced examples of every car I suggested.
There's a guy in my area who's run a 4 door automatic camry for 2 summers of autocross and 1 of HPDE.
Has had a blast, found out he like track days well enough, and popped for a spec e36 to carry on.
I think mazdadeuce/woody are onto something with the trackccord game.
Also - take a look through a few of these albums, these guys take great pics and try to get every car that turns a lap. It will show you what cars you'll be sharing the track with (at least in the mid Atlantic area). HPDE has some obvious trends but plenty of others that I wouldn't have expected.
http://www.finishlineprod.net/nasa/index.htm
In reply to Snrub :
Its not accurate to say I’m not thrilled with the suggestions I’m getting. I am.
I was merely pointing out a Mk1 MR2 SCCA ITB car isn’t even close to what I was asking for. Nor is an RX-8 anyone’s idea of a family-friendly daily driver.
I truly appreciate the effort though.