@Anna L. I agree wholeheartedly with @Michael Dumler, make sure to get a copy of the HOA bylaws and covenants, so that you are aware of the rental restrictions if any. The 3 properties I have( 2 condos and 1 townhome), before signing the contracts I found out with the rental regulations were with the HOA and what things to do they cover, versus me, because you also want to make sure that the tenant has a copy as well, so that no fines are incurred. It's really not that bad, you just have to read through it, so that you know the do's and don'ts. Depending on how parking is set up, they have restrictions on that, animals, common areas, noise, etc.
Vacancy just comes with the territory, we would all like to have our properties rented 100% time, but at least for me starting out, that's not the case. On average it has taken me about 3 weeks - 1 month to fill a property, but it is usually with pretty stable tenants. I try to be as diligent as I can on the front end with screening tenants and then finally getting to the approval phase, that it takes me a little longer, plus I am new at it, but I account for it when analyzing a deal and make sure I have the funds to cover the vacancy. Hopefully as time goes on I can reduce the time, but not the screen process.
Don't second guess yourself, YOU GOT THIS! Good luck and congrats on your offer being accepted. Now the fun begins, :-).