@David S.
I remember the feeling, we all have been there and it takes time to get comfortable (in hindsight you will wonder what you were so worried about). It does not sound like you are stuck in analysis paralysis, rather you feel the pressure to make something happen. You are doing the right thing by running the numbers. The more deals you analyse the better you will get spoting a gem. The old rule is: look at 100 properties, offer on 10 and get 3 accepted. Buy one. Follow this rule!
Sounds like you are already looking at deals, if you have not looked at at least 20 I dont think you are ready to make an offer. And you dont have to go inside every house. What I usually do is I make a list of 10 potential deals and then do drive bys by myself. Typically I can tell from the outside if I am even interested in the deal. This way you dont waste your realtors time. (by the way, if you are not happy with her, find someone else - seriousley, its your money on the line, not hers and you want someone who either works a lot with investors or owns rentals. You can always pay her for her time if you want to.) I schedule showings only for properties I like from the outside.
Your next goal is to get 7 out of 10 offers rejected. This is going to be hard, because you will feel the urge to make a "good" offer and get it accepted. If you get your first offer accepted you are offering too much. You want to be rejected and that is certainly counter intuitive. I am not suggesting to make redicolous low ball offers, but you should ignore the list price and come up with your own math for you purchase price. Getting your first offers rejected will also make you a lot more comfortable with your position; you will feel a lot more confident with your first accepted offer.
Once you have an accepted offer it is time for a thourgh inspection. Have a good home inspector ready and go with him and have him explain the issues to you on site. He will tell you what real problems are vs. things that are easy to take care of. If something serious or unexpected costly comes up don't hesitate to walk away from the deal or adjust the price.
You dont need your first deal a spectacular one as far as cash flow or cap rate. If you make $150-200 per door after PITI, PM fees and reserves you are doing well. The most important thing is that your first deal is a safe deal. Buy a solid property in a desireable neighborhood. You will have to pay a little bit more and there is more competition, but once you own the place you are on the other side of that equation. Easier to rent, more rent, less vacancies and if you want to sell you will be able to sell it faster and for a better price.
Remember location is the only thing that you can't fix. If you are in a good neighborhood where people want to live and you have a nice place you will never have an issue keeping it rented. There is something to be said about investing close by and five minutes sounds much better than 30, but a direable neighborhood is more important. If your cash flow is a little bit less I would not worry about it, as long as it is positive and you know your deal is solid.
Expect your first property to be a learning project. I think the main goal for your first deal is not to make it the best investment ever, that will come later, just make sure you stick to your numbers and you wont have a problem sleeping at night. Good luck!