Thank you for your service. You are definitely no stranger to hard work, so there's plenty ahead for you!
Ballpark. $100-$150K more if you are extravagant. This includes build-out, equipment, wares, tables, chairs, training, and cash reserve. Differences would be mostly type of counters, table tops, lighting, that sort of thing.
If you can do all your own build out, or if you can trade for it, I would guess it's about $30K less.
First step. Find your local Small Business Center, it should be associated with a local college or the city itself. This is a great starting point.
Step 1a. Gather information. Visit coffee shops. A lot of them. Know what you like, what you don't like. What seems to work and what doesn't.
Step 1b. Plan and execute. Use your above knowledge to plan your ideal shop from the ground up. Understand your reality. The truth should be just a hair beyond what you think is possible.
Step 2. Look for spaces to lease. Think about location, size, price. Don't fall in love with a location. It can't love you back. There's always another deal you may have missed.