It is always more difficult at the beginning. Here are my answers to your questions.
1) Yes. You would want to deduct the mileage every time. I tried to make things a little easier. So I usually find the distance through Google map and just record the times visited the property. I am not an accountant, but I think as long as you have some documents to explain where your number comes from, it should be ok.
2) We set up LLC before close. It saves you some money for title transfers. No tax issue on transferring the property from your name to LLC. When we set up LLC initially, it was for legal protection based on other people's suggestions on the forum. However, when we start to advertise properties for rentals, I realize a LLC sounds much more professional than a person's name. Good quality tenants tend to prefer more professional sounding companies.
3. If you have not tried Postlets yet, you should try that first. That is usually my starting point when I need to create a new ad.
4. Allstate has the best prices I have seen. However, they could only sell you insurance for maximum 4 rental properties. More than that, you need to find a different one.
5. We use MrLandlord.com to do credit checking. They only charge $9.95 for the service, which is the lowest I could find online. We have been in rental business since 2011 with total 12 SFR rental properties. We have a very good track record of quality tenants. I must say MrLandlord.com's credit checking has made our decision process much more reliable and consistent. We also use eRentPayment for collecting the rent on almost all of our properties. They have excellent customer service with very reasonable price.
Wish you good luck on your first leg of journey!