If a car needs an alignment and new tires, which one do you get first?

It doesn't matter as long as you don't drive very far with the new tires and cause wear patterns to form on them before getting an alignment. You can align a car with the old tires just as well as with the new tires.

tires...and then alignment

new tires then alignment

Both. If you're strapped for cash and the tires are so worn as to be unsafe, I second what 'Mitsubishi Master Tech' wrote. Get the tires first, then have them aligned as soon as possible. This is because once uneven wear begins on a tire, it usually continues to wear that way until it's fubar.

So getting an alignment after you've let you brand new front tires rub bald on one edge due to pooh toe in, is sort of like very carefully locking the barn door after the horse has bolted...

Same time, just like changing the oil filter with an oil change. It's not rocket science.

I replace My Tires and a wheel Balance after which i always get a wheel alignment

even on the BMW motorcycle i check alignment after Fitting New tires

Tires first.

Tires and it's best to keep the alignment receipt that has the mileage on it. Get the alignment with in 100 miles from the day you install the tires. It's hard to align a vehicle that has bad tires. When you test drive the vehicle you don't know if the alignment or the tires are bad if it pulls.

Same time.

Tires, since the size, profile, tread depth etc. may affect the alignment. But as others have said, if car is severely out-of-alignment, tires can be worn quickly so you only want to drive a few days before getting it aligned with the new tires. Tire installers typically over-inflate new tires to seat them - so check and adjust the tire pressure before the alignment.

Alignment. If you get the tires first and wait, a bad alignment will cause premature uneven tire wear.