First, there is some confusion on what you want - stating the bullet caliber doesn't tell us what cartridge your using - 7.62 x 39 or 7.62 x 54. Since it appears you have the AR15 lower, the larger one obviously won't fit. 7.62 x 54 uppers are a couple of inches longer, and a budget build on one is a real trick.
Assuming you meant 7.62 x 39 - the Russian AK round - again, budget build is a nice goal, but the caliber won't help much. There aren't a lot of suppliers in that caliber. Magazines aren't plentiful, the bolt is a specialty, and the barrel is had by a few - which has put you at the mercy of the few suppliers. All for the sake of cheap ammo.
Be careful there, historically low prices on ammo are that - a bubble in time. .308 used to be cheap, no longer. Blasting a lot of cheap ammo really isn't, and you get exactly that, performance based on milsurp or import, not the latest developments.
Bang for the buck means downrange performance to me. The 7.62 x 39 is a large, slow, blooper round seen on the range, with more than a few feet of drop at 300 yards. It's not a flat shooter, it's relatively slow for a cartridge, and guessing bullet drop at various ranges is a challenge. It's usually loaded in military rounds - not hollowpoint, so it will penetrate, but not expand.
The best comparison is that the 7.62 x 39 is just a rimless .30-30. After all the work and effort of building an AR, you won't get any better performance downrange than some old guy with a corduroy hat shooting his Winchester lever action on the next lane.
As said, a different caliber would give you different results. 5.56 would give you much flatter trajectories, 6.8 would give you 400 yard range and good lethality in a 16" barrel, 6.5 would give you 600 yard paper punching accuracy in a 20" barrel, and so on.
With the number of options out there, the build will turn out ok pretty much whatever you do. A good long look at what you'll really be doing with it, what caliber gets that job done, and how much you can spend leaves you using the 5.56 for the best bang for the buck. After that, everything is more expensive, and that means looking at what ammo costs are going to be like in the next ten years - not today.
Again, study the ballistics of each cartridge to match what you want in downrange performance, then build to that. It's not how cool the tool, it's what the results are.