Get yourself pre-qualified for a mortgage, it doesn't commit you to that mortgage company, but it helps you get your foot in the door as some realtors and sellers don't want to spend the time on non-quals and dreamers.
Plan on closing costs to be WAY over the estimates. You are going to be paying some portion of the property taxes, plus a real estate transfer tax, some legal fees, 1st years homeowners insurance right up front, etc. Our closing costs came out around 10K...really.
I'd plan on having at least that much in ready cash available to meet those costs. You will also find that there will be immediate repairs and upgrades you will want to carry out. Things that were not serious enough to get in a battle over with the sellers, (not issues of code or safety) or are simple matters of preference. Those costs add up. Things like lawmowers, snowblowers, etc. tend to pile up.
If you've got the scratch, put down the full 20% needed to get past PMI. Make as big a downpayment as you can make, as that lowers the loan amount and the amount of interest you will pay. If you can swing the higher payments, a 20 year loan will cost you tens of thousands of dollars less over the life of the loan in reduced interest payments. BUT, if you would have trouble paying the payments, you should go with the 30 year, interest is pretty cheap these days.
Other things that will be wrapped up into your mortgage: Most lenders will want to escrow your homeowners insurance and property taxes. They will roll the annual premium costs into your payment schedule and pay those fees automatically when they come due. Part of the closing costs will be a pre-payment to seed those escrow accounts for the year so that the mortgage company has something to pay those fees with. Tax revaluation will usually not screw up the payment plan, you'll just get a supplemental tax bill for the amount not covered by Escrow. All this makes owning a home more convenient for the homeowner, at least so long as they have a mortgage, but often leads to painful sticker shock when they pay off the mortgage and the tax and insurance bills start showing up at the door and need to be paid directly. All those tax adjustments and revaluations that occurred over 30 years, and which you saw only a small fraction of, hit you full in the face and you are paying 45 bucks on the thousand of assessed value per year. Have a house assessed for tax purposes at 200K? Your tax bill is 9k per year. OUCH! Fighting excessive property taxes at the municipal level is important!