First off- Howdy from Cut n Shoot, TX! 

I'm looking for opinions and/or knowledge on what may be the best breed or mix to both jump and run barrels? 

I'm mainly a jumper, Hanoverian's being my weapon of choice. 

Looking to purchase a new partner in crime to do more barrel event types, though I would be remiss not to have one able to jump as well.

cheers!

There is some very talented hunters in all 3 of the stock breeds....AQHA, ApHC, APHA.  Many of them are almost too specific in their breeding to be really talented at the barrels, but that is the beauty of the 4 and 5D format.  You can still be competitive in the lower divisions and take home a check.  My Dash Ta Fame stallion stands 16.2 and I I could run barrels and poles on him, ride a pretty hunter round, ride lower level dressage tests,  chase cows, do Cowboy mounted shooting, etc.   Is no reason you can't do both on the right horse.

Thanks for the advice! Also sent you a PM

We've bred so much race into a lot of the quarter horse lines, that you could get away with doing both. I have an appendix mare thats 16.1 (Marthas Six Moons/Firewater Flit/Beduino bred) and I've had several friends that event and do dressage, beg me to let them get on her in their gear. She moves and looks like a dream for english. I would bet you could find something in the appendix world that could excel in both. I used to jump in college and might try her out someday myself, but for now I'm focusing on patterning her on barrels first. You could also try an ottb, there's quite a few successful at barrels in the world as well as jumping. 

Hello & welcome to BHW!