As long as the gun is safe and functioning properly, it is acceptable for IDPA use. Having a gun that is more accurate than you can drive it will eliminate one often used excuse on the range: it's the gun!
Fitting a new barrel and tightening the slide to frame fit will improve accuracy. If the smith plan to use a Bar-Sto gunsmith fit barrel, then $305 + tax is a good price considering the barrel alone cost ~$200 retail. You may also want to ask about a new slide stop. If the existing one is worn and looks like it may need replacement down the road, you may want to spring the extra $20-$30 for a new one so it can be fitted to the barrel. The lower lug of the barrel should be specifically fitted to the size of the slide stop cross pin. That's why if you need to have it replace, it is best to do it when you replace the barrel.
You should also expect to have the barrel bushing replaced as well. I suspect the current one will be fairly loose in the slide. An accuracy job will fit a new bushing to the slide to just a little tighter than hand tight. The inside diameter of the bushing will be fitted to the diameter of the barrel. If you have a preference on how tight the bushing will fit, you should explain that to the smith. Some people don't like to use a bushing wrench to disassemble the gun. Others don't mine. Your preference will allow the smith to adjust the fit accordingly.
Also make sure you and the smith understand what you intend to use the gun for. The level of accuracy and how tight the parts fit will vary. A competition /bulleys type gun will tend to be more tight than a carry gun.