Edit: I missed that my location and OP's location are different. Probably general advice is still generally applicable, but OP should check the specifics for their location.
- I need to bring my credit score to at least 630 before lenders will even talk to me.
Whether this is true depends on a number of factors. However, the higher your credit score the more likely lenders are to talk so it's always good to improve your score if you can.
- I need to finish paying off my car which I still owe about $4,000 over the next 2 years.
This isn't necessarily true and depends on your exact financial picture. The mortgage lender will want to make sure that your total debt service load, after adding the mortgage into your mix, is less than a specific percentage of your income. IIRC, it's 30% or 40% of your total income is the upper limit. Ask the lender, they will be very forthcoming with this information.
If your total debt service load is greater than that, but, would be less than that if your car loan is paid off, then paying off your car will allow you to obtain a mortgage. That's a very narrow window though.
It might also be that your specific financial picture includes no other credit history than the car loan. In that case, I could see a mortgage lender wanting to see the loan paid off as an indicator you're likely to pay off your mortgage. This is speculation on my part though.
- It's typically a 30 year term.
As others have pointed out, mortgages come in all sorts of lengths for all sorts of reasons. Others have also noted that generally you don't want a longer mortgage, and should prefer a shorter mortgage. I haven't seen anyone mention why: the longer the mortgage amortization, the greater the amount of interest paid. For very long mortgages, you can easily end up paying more in interest than the original price of the property. Prefer shorter mortgages amortizations where possible to minimize your interest cost.
How committed should I be to 30 years? I mean, suppose I live there for 5 years and need to move. How hard would it really be to sell the house? I mean, I assume this is a normal process, so the real question is, what are the options?
Selling while there is an active mortgage probably means paying a penalty for early paying-off of the loan. Ask your mortgage lender for the details around this, they will be very forthcoming.
On that note, if it was easy to sell a home in this situation, then what would stop me from extending the terms to, say, 40 years? Higher interest? Higher credit score requirements? Just rhetorical...
If you're considering flipping the property, that's a specialized circumstance in which you might prefer a longer amortization period to get the current payments down to preserve cash flow for other purposes (like renovations).
If you're considering buying a home to buy a home, prefer shorter amortizations with as high payments as you can stand, to minimize your interest cost. Minimizing your interest cost is a life-time length situation that not everyone is equipped to think about.
Source: paid my own (first and only) mortgage off. I had the same qualms re: selling with a mortgage. It turns out you're not likely to move in the next five years (typical term length) if you don't currently think you might move.