What type of financing are you going to apply for, FHA, conventional, USDA, etc? I would wait until you resolve the collection issues and have at least some money in savings. There have been some on here that have stated they were denied or having problems obtaining financing because the credit report showed there were disputes. Have everything resolved that you plan on. It is much easier to get credit approved with the condition of showing funds then it is having money but credit issues (if that made any sense! lol)
You don't want to apply to early or your documents may expire and then it will be like starting over. If you plan on closing in September then I would suggest applying approximately 60 days prior to. That should give you plenty of time to get your credit approval and start looking at properties. About 90 days out, I would contact your local housing authority or a lender who works with the housing authority and ask them the turnaround time on their program. This would be the one thing that could hold up the process is if they are very slow. Also, with FHA, they probably won't even make you pay the medical collections because they are so old but that is also going to depend on the amount owed on them. You may want to work on getting those resolved outside of using the CRA's. That way they won't show as disputes on your credit report. I would go check out the medical board