If you're still pre PPL, then I suggest what you are looking for is an aircaft you can complete your IMC rating and exercise your rating. For this, a PA28-140 (which is what you're looking at with your budget) would be ideal. If you are later (and this I suspect would be much later) looking to do your IRs, then think about trading up.
But when it comes to groups, here's some benefit of my experience having been a member of a few.
1. A private CofA is adquate for post PPL and a bit cheaper than Public Transport.
2. Limit the number of members to a maximum of 8. Any more and you will have problems with utilisation and personalities.
3. Have a set system of rules for booking. An internet web site with a booking page is best. It's a pain in the bum when you've just driven 100 miles to find the chap who took the booking entered your details on the wrong page of the diary and the aircraft is in France!
4. Have a set level of experience for members joining. I suggest 100 hours post award of PPL is realistic. I know this won't apply to you as you will have yet to finish yours, but I suggest any future joiners should be restricted.
5. And while we're on this subject, have a set of rules in place to ensure that when members leave the group they only sell their share to people acceptable to other members.
6. Price you hours realisticly. Run an engine fund with the intention of replacing the engine at 2000 hours. Don't expect the engine to last more 'on condition'. With several people flying it, it won't! And when buying the aircraft, get one with plenty of hours left. The price you pay to fly will go up if the engine has 1800hrs when you buy it. Also, add some extra cost to run a fund for contingencies.
7. Set the group up as a Limited Company with each member owning a share in the company rather than a share in the aircraft. This is easier and cheaper than you think and will stop your aircraft being sequestrated if a member is declared bankrupt. It also gives you some protection if anything drastic goes wrong, but the members who volunteer to be directors have some liability.
All these recommendations come from hard experience! And expect to fall out with your group members from time to time - even if you were good friends when the group formed!