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Since you're a first time homebuyer it might be best to use the program in your state. If you're not buying rural property it's usually the best option and only requires 3.5% down.
Things to keep in mind when looking at houses:
Sellers will expect you to have "Earnest Money". You give this money to the title company and they hold it in an escrow account. There will be conditions in the contract on how the money is handled but it's usually non-refundable after your inspection is complete.
First time homebuyer programs only require 3.5% down but come with mortgage insurance requirements which can add hundreds to your monthly payment.
USDA loans are similar but with 0% down (they only apply to houses in rural areas).
Your lender will approve you "up to" a certain amount. You will end up taking out only as much as is needed to cover the house with your down payment and earnest money. There's no reason for you or your realtor to tell the seller/their realtor how much you were pre-approved for (they only need to know that you were pre-approved).
Take your time, some realtors will try to push you to close quickly. They want a fast sale more than they want the right sale.
Sellers and their realtors will use shady tactics such as claiming another offer came in after you make an offer to try and get you to bid higher. Don't panic bid and don't get too attached to the prospect of a particular house.
This is your first house, not your forever home.