If your needs are simple, anywhere that has competitive prices and service, a tire in stock you are ok with, and can get you on the schedule. Walmart is ok, so are a bunch of other places.

If you have awd, you need matching tires all the way around. Otherwise, you can just change front or back.

It's ok to get cheap new tires. Especially if you think your car might outlive your tires.

If you have front wheel drive, and you almost certainly do, it's best to put the new tires on the front and rotate the older ones to the back if you aren't changing all four. Winter is coming and you will get better traction. Besides, they wear faster on the front.

It's not 100% necessary, but go ahead and get the valve stems changed unless you changed them pretty recently. It's cheap insurance. Some places will include it, others will charge.

They may charge you extra for balancing and mounting. Normally they will quote it that way, but make sure if you are comparing prices. And yes, they need to be balanced and mounted.

If you are offered a road hazard upgrade, or similar bs, it's up to you.

If you can afford it, go ahead and balance any tires you don't change while you are there. It will ride better and give better wear. If you never get to highway speeds, it doesn't matter as much.

Before you change them, check to see if your tires are wearing evenly. If they have weird wear, you may have mechanical issues in which case you may be able to get them to take a look while it is on the lift and at least let you know what is going on.

If everything seems tight mechanically and you are getting weird wear, they will probably tell you that you need an alignment. If they can do it, go ahead and get it done. If there are repairs, they will likely have to do those first and then do the alignment.
Some places will check your brakes while the wheels are off. Some places will try to scare you into brakes and brake parts you don't need, but it isn't a place to skimp either... If they show you and you don't know what you are looking at, maybe take pictures to show someone who does.