No worries...gotta start learning somewhere sometime.
For p-dogs and for long-range use out to the effective range of a .223/5.56 AR at mag-lengths, the v-max is a good choice for the doggies, but for longer ranges, you'll want to move up to heavier, match type bullets like the 75gr and 77gr offerings for example (Berger, Sierra, Nosler and Hornady all make good fodder in that range for reloading purposes) with the higher BCs that will actually perform at extended ranges compared to the lighter, varmint weight bullets which do NOT. Having shot more than a few varmints with the match stuff before...it'll more than do the job and work far better for you at the longer ranges (unless the laws in NE prohibit you from using "match" or like ammo for hunting purposes that is...even vermin control).
As for barrels...I'd opt for a 1:8 twist which should allow you to run the heavies that I mentioned, right along with the middle-weight 50-53gr V-maxes.
Since you won't be running and gunning with the rifle, and your hunting won't involve a lot of humping the rifle all over the place, I wouldn't be too concerned with weight or length of the barrel. There are laws of diminishing returns with extremely long barrels, especially on an AR, but I'd suggest at least a 20" tube (or up to 24" if you don't mind more length/weight) so that you get the most MV possible with the heavier pills for longer range use. As for the chamber...that's your call. I'd personally opt for a Wylde chamber rather than a .223 Remington (Match or otherwise) or a 5.56 NATO chamber as that will give you the best of both worlds so that you can safely and accurately run both .223 and 5.56 loads/ammo.
Cost effective is a relative term, but custom will ultimately get you the most accurate barrel combo possible, as well as ensure that it is properly headspaced to your existing bolt if you provide said bolt to the barrel maker who'll do the work for you. If you go that route (and don't mind a LONG wait), then companies like Krieger can set you up with one of their Varmatch barrels for a very reasonable cost (again...reasonable is pretty subjective). There are numerous other custom barrel makers that can probably assist you...if you want to go that route, I'm sure that I and many others here can point you in the right direction. Whatever you do, I recommend getting a matched/headspaced bolt with any new barrel whether you go custom or off-the-shelf, or at a minimum, if you don't, get your headspacing checked out if you elect to save cost and run your existing bolt with any new barrel.
In terms of production barrels, there are a whole host of options. White Oak Armament is an excellent sources for some of the best AR barrels on the market, but their lead times are roughly 5mos out at this point as they are still recovering from the surge around the first of the year. They offer excellent barrels in a variety of configurations (and are also stocked at some of the retailers mentioned momentarily). You can also often find Krieger barrels in stock and ready to ship from places like Brownells, MidwayUSA, Fulton Armory, etc. Always a good option as their barrels are among the best in the business. Also, in addition to aforementioned sources...Rainier Arms, DSG Arms, Bravo Co and many other major AR retailers stock some high quality barrels, including Krieger, Criterion, Lilja, etc. in a variety of configurations. Have a look at those spots and see if anything strikes your fancy.