I have been doing boneless skinless chicken breast(BSCB) for years (my wife though a country gril, hates chicken on the bone, skin or dark chicken meat). I do BSCB dry seasoned, brined, with sauce, plain just about any way you can do BSCB on the grill(gas, charcoal or smoker) I have. Meat wise I just buy the ones on sale-- large family pack, 4 to pack etc with out regard to thick or thin small or large breast. Get a good sale on them and I have bought a bunch (like 40-50 breast) seasoned, brined, grilled smoked and I vac seal in 4 finished breast per bag for future use. Biggest thing I started a several years ago was cooking to temperature and timing vs cooking to I think its done(usually results in dry tough chicken).
BSCB -- what I do: Dry season, marinade, brine as you choose.
Grilling -- get the grill hot 450-550 degrees -- grill on each side 2-3min (do a 45degree turn at 1-1.5minutes not a flip over but turn get some good grill marks). Adjust temp in grill to 350-400 and/or have a indirect heat area on your grill (gas I lower all burners and let temp settle, charcoal I adjust vents and have indirect cooking area). Now its just time and Internal Temp (IT) of the BSCB and you check those as you see fit. IT for BSCB you looking for 160-170, keep going into 190-200 degrees and you will have dry tough BSCB(chop that up and add BBQ sauce for BBQ chicken samich).
Smoker-- for BSCB I get the smoker rolling all vents open it hits 250* I load it up and smoke a way. Pull the BSCB at IT of 160-165. I usually smoke I have on chicken, pork butt, beef, turkey some combination of 2 items or all four or just several of 1 item. I run the smoker at 225-275(most times try to settle on 250) and check IT along the way. If just doing BSCB on the smoker not to bad check IT after 2hrs and forward, watch where the BSCB thins for drying out. Smoking or grilling meats of different animals with different fat levels at the same time requires more monitoring. Meaning smoking a 9lb pork butt and 10 BSCB---don't expect the BSCB to take the same amount of time as the BUTT..or be as forgiving in temp/time changes as a Butt.
Remember add BBQ sauce (not a mop) -- the last 5-10 degrees or so for the meat--it will prevent or lessen the BBQ sauce burning vs caramelizing on the meat grilling or smoking.
Here is the link to USDA safe internal temperature of meats. But also remember when you take the meat off the grill/smoker to rest the IT will rise 3-5 degrees. I have had no issues pulling BSCB at 160-165 IT, let it rest 10-20min and yum yum up. Also doing a whole chicken, beer can, split or bone in chicken parts is easier too. BSCB will dry out on you real quick..same with a pork tenderloin or beef tenderloin.
https://www.fsis.usda.gov/wps/portal/fs ... t/ct_index