I signed the contract and got an inspector in the next day.

If you have a trust worthy cleaner, handy person, and a local inspector, I would self manage.

Inspections are good start, but they don't check anything that the inspector cannot see so once you start opening walls, you might be in a big surprised.

Quote from @Nicholas Jacob Nowosielski: Hi all, Can anyone recommend a good, and thorough inspector that can walk a few properties for me and make a list of things that need to be done before I call out the section 8 inspector to come out? 

Get city inspectors involved in any of that and you can add 25% to the cost.

Does the realtor have a good team behind them (lender, home inspector, contractors)? 

They might not always make the best decisions, resulting in failures, but some of those decisions were driven by bad data (whether from the borrower, appraiser, inspector, or whoever).  

(Approach - 2) - He says that if he is asked to pull permits, he is not responsible for any additional work that the inspector may throw (basically more money out of my pocket on the rehab costs).

My wife and I have been investing here since 2015- we do several flips a year and have 20 rental units we self-manage.I'm a licensed Home Inspector and licensed General Contractor. 20 years in the trades.

Note that most all lead inspectors will do dust swipes (Lead Safe tests), but not all have the equipment required to do Lead Free testing so be sure you're specific in what you ask for.