The spending part should be the most easy to critique so it might help if you detailed that. Right now I'm seeing
400 towards rent
100 in savings
100 towards trips
100 + 200 towards car loan
which only accounts for 900 from a take-home of around 2000/month (you can provide the exact number). These all seem reasonable so the missing ~1100 is where people could comment.
As for where to open an IRA, Wealthfront has a minimum of $500 and does not charge any fees until your accounts is over $10k (If you used
this link, I think that number changes to $15k). What I like about Wealthfront is that they choose a balanced mix of low-cost ETFs for me, as opposed to the more haphazard way of picking and choosing that I was doing before.
As a last comment, I would suggest you put $2000 at the very minimum into an IRA over the whole year. You would be eligible for a $200
Saver's Credit on your taxes, which is an immediate 10% return.
EDIT: a review of wealthfront
here. If you end up getting an account, you should use someone's (anyone's) referral link for the reason I stated above. As I've already received this benefit, it won't affect me further.