Pros & Cons of Buying an Integrated with Built-in DAC?

Buy the best 2 channel integrated that's in your budget without a phono stage or DAC. You'll always be better off buying an outboard phono and DAC than a Swiss Army Integrate. Look for something used like an Ayre, Pass or ARC and you'll be happy. 

My kids use an iMac at home and for the kids it's just fine. I look at an all in one integrate as the one box computer, being an Apple or a HP. I prefer to have my computer in separate boxes so if my monitor takes a dump I'm not totally out. No iMac or one box PC/Monitor machine is ever going to outperform a workstation and standalone monitor for the same money. 

There are many nice integrated amps out there with onboard DACs and etc. Can you likely for the same money put together a better combination with a few boxes... yep. Plus if you want to upgrade to a better DAC, experiment with cables to find the sound you prefer you can customize or tweak the sound to your liking as you change out speakers or other components in the future if that happens. 

There's no right answer as some above have noted and you should trust your ears and not the advice of others in the end. Try to drag equipment home from local shops if you can, or buy gear used and if you end up not liking something resale it it likely losing little if any. This is hobby and in my experience part of the fun is experimenting with gear and chasing to put together the best system you can afford. If you want the all in one solution and really think this is the last purchase then maybe this makes sense. 

Best advise is visit some stores and listen and hopefully you can demo at home. If nothing too close to home, then make a road trip; it's a lot of fun visiting new stores.Trust you ears. Good luck.