What kind of home loan should I apply for?

You have been misled. Your good credit score is not rewarded with better interest rate, just more borrowing options if you can meet all loan guidelines. Plus those types of loans that bypass PMI all went away after the housing crash.

I suggest you compare the state program, that likely utilizes FHA loans with a conventional loan from a traditional lender. FHA loans will have a slightly higher rate and closing costs, but that state program you found also likely comes with down payment/closing cost assistance (carried as a small second mortgage that you don't have to repay) which offsets much of the expense of the rate and closing cost difference. The way to compare is by getting a good faith estimate from each and crunching the numbers. In fact you might want to get a third GFE from another conventional lender to keep the other one honest and competitive too. The conventional loan will require 5%. And don't forget it may be possible to make an offer on a house that is contingent upon the seller conceding some money towards your down payment and closing costs too. But that is something to talk to your buyer's agent about.

there's a LOT more that comes before applying for a loan, like a good income, good credit, downpayment, etc. I think the 30 year are the best.

I must have responded before you answered your question...At 24 you don't need a home. A home is used for children, pets, status, maybe for helping your elders in the family live with you. At 24 there are many chances you'd be moving for a good job. What is your income now? You don't sound ready to me. Work and save up for your downpayment, for costs at closing, get yourself a car and get it paid off, get all your schooling in and paid for, and "then" look toward a home. Homes don't appreciate like they did in the past, plus with climate change a lot of people end up with their homes flooded out and lost so probably your home insurance and flood insurance (that's two different things) and taxes would eat you alive.