Ask them how many banks/lenders they work with the more they work with the higher chance you have also keep in mind PreOwned vehicles no matter how great they are come with a higher apr/payment 9/10 than a New vehicle. See if you can get approved through your current Bank/CU FIRST and take that to the Dealership if possible to help keep you from getting a ton of inquiries some places will do their best to keep it low while others will hit you with 70+ inquiries with no cares in the world. 600's is a good place to be 650 and higher would be better but make sure also you are reviewing your Car/Auto Scores and not your Bank Scores. 
If you can get that collection removed that would help greatly. They tend to not care about Student debt or Medical Debt (doesn't seem like you have Medical?! unless that is what the Patients First is?!) Once your cards hit the 6 month mark that will help too. And also I can't stress this enough if you do get a PreOwned GAP GAP GAP and EXTENDED WARRANTY lololol.
No problem sorry for this late reply but Check out what it says is hurting your score if it is something like to short of history that you can only help with time but if it's something like High Utilization then of course that you can work on ASAP. I'm not sure what state you are in but for example my state (Ga) the dealer I work for our average customers are lower to middle 500's BUT we also work with over 52 different banks and lenders so that is why I mentioned before see how many banks they work with (I still stick by the check with your CU or Bank FIRST) to avoid extra hits that may be not needed....but if the dealer works with more lenders it does make them able to be more flexible when it comes to programs, negotiating price, credit ranges etc....So if the dealership you are looking into only works with 10 or less then I would def. shoot with trying to get your own Financing as they wouldn't be as lenient or may not be able to offer some things as someone that works with over 20 etc. Is the 598 your middle Auto?!
But removing those collections will def. help a month or a few months after removed for sure. You may see a drop at first since it may affect your Age of information BUT it will help in the long run most definitely.
@Anonymous wrote:
Honestly, I don't believe your scores are high enough and you don't have comparable auto credit for a lender to loan you out $20k+
as a first time buyer a bank's realistically going to want you to be at $15k amount financed or less.
It all depends on the dealership honestly you would be right that being a first time buyer it will be a bit more interesting but again it all boils down to the dealership in question...Ex. we have First Time Buyers Program at our location and have helped students with 500's CS into a vehicle that is right at 20 a few over 20k depending on what they have to put down etc....If they don't have a program like that or only work with a handful of lenders...it will make it harder....just do your homework on the place with the vehicles you are interested in. 
