Use the oil based Kilz if you're going to use it. A lot of professionals were poo-pooing kilz but it seems to do it's intended job.. prime a paint's surface. 5 gallons went much farther than I ever thought it would and it covers stains fairly well though you don't have to completely cover up every last trace of old color or stains with a primer.
If you are actually painting properly.. meaning priming first, make sure your finish coat is actual paint, and not a paint and primer combination. It seems like a lot of people these days complain about paint being thin or requiring lots of coats, and from my research that seems to come from paints that advertise being both a primer and paint in one.
If you buy a paint that is just paint it will likely be thicker and cover better. If you're going to do multiple coats anyways might as well do a layer of kilz followed by a good thick paint like Sherman Williams Cashmere, which when on sale for 30 or 40% off will be significantly less expensive than the Benjamin Moore equivalent and work just as well if properly primed.
Keep in mind oil based kilz does release odors and you'll want a window open. I'm normally pretty tolerant to chemical odors but oil based primer gets strong in enclosed areas. When I had the lowes person try to mix the metal container it leaked so I suggest just shaking it up when you get it home.
Paint is a lot like engine oil, lol.. people with a casual knowledge of the topic will come around and say that today's paints and oils are so much better than ones from 15-20 years ago because of all the "additives" but they never mention what these additives are, and I don't recall any vehicle engines exploding or people's houses falling apart 20 years ago from all this badly engineered paint and oil we had. I always laugh when I hear people say this. If paint is that much better, use any old brand.
If anything the paint/primer thing has deteriorated paint quality in my opinion in an attempt to save time when it usually doesn't. Also since the envio-nazis required more environmentally friendly road paints, ever notice how they rub completely off after about 8 months and you can't see where the lanes are? Seems like a regression to me.