There are a lot of factors. For example, how large do you want to print? Are you looking for high quality B&W prints as well?
And what is your expectation of 'high quality'? You can can get pretty decent prints on cheap 'photo printers', but if you really want top notch quality, those printers can get expensive. Keep in mind that there are other factors to making your own great prints. Use good quality ink, you probably want archival rated. The paper you use can make a big difference...and for each paper type, you may need the proper profile. You may want/need to do a bunch of calibrating and test printing to get the results you want.
IMO, it's just easier to use a good photo lab. It's their job to make high quality prints and you don't have to worry about any of the hardware issues. Prices these days are really competitive, so if you compare the costs of printing at a good lab vs buying a printer, buying high quality paper & ink etc, then it's really not much more expensive to use the lab. It may even be cheaper.
Keep in mind that whether you print at home or at the lab, the first step to getting the prints to look how you expect them (besides taking the photo) is to calibrate your monitor. If your monitor isn't properly calibrated, you really have no idea if what you are seeing, is actually how the image file looks.