After putting together the AP necessities forums, I decided to list some budget players, going off the AP necessities.
Budget is 50K per position (XBox Market) (Powering up is added into budget)
QB - Mike White 91 or Derek Carr 92: Both get SFL and Fearless for 5 AP. Yes that's a lot of AP but you need Set Feet Lead, and Fearless will keep your throws accurate under pressure. They have similar stats, but Carr has a slightly better release. White ends up about 25k, and Carr is about 45k.
HB - 93 Breece Hall: While right at that 50k budget, this card will play great. 93 speed, 220 pounds, has all the stats you want (besides catching, those are a bit low), and can get Short In Elite for 1 AP.
FB - 91 Christian Okoye: You don't need much for a fullback (or a fullback in general with Csonka being a captain), but roughly 40k, this can be a beast of a fullback. His AKA Vanguard for 1 AP flattens any LBs or DBs he blocks, and 88 speed is still good for a 91 card.
WR1 - Garrett Wilson 92: Right at that 50k mark, this card has respectable speed at 93. But what makes this card a true WR1 is his 2 AP Route Technician. Route Technician will create separation on any route involving a cut, making him a must-have for budget teams.
WR2 - Adam Theilen 92: Another Christmas card, Thielen comes with 93 speed and a respectable frame (6'2, 200 lbs.), what makes him a true WR2 is his abilities. He can equip short out elite for 0 AP, and 1 AP short in Elite in a separate slot. Those 2 abilities combined will enable him to run very effective short routes, as well as boost his catching in these short routes.
WR3 - Zay Jones 92 - while only 6'2, paired with his 1 AP Deep Out Elite, that should give him what he needs to win some 50/50 balls against smaller DBs. Deep Out Elite will also provide some separation on deeper routes. That 92 speed isn't the greatest however.
WR4 - 92 Mecole Hardman: While Mecole is the fastest WR on this list with 94 speed and is about 40k, he doesn't get any discounted abilities. But that speed itself should get some separation. Just don't expect a whole lot from this card.
TE - 92 Evan Engram: This TE can do just about anything. He has 91 speed and can get Short In Elite for 1 AP. The only issue with Engram is that he can't block (67 RBK) and he's 6'3, short for a TE. But he should get the job done for 40k
LT - Andrew Thomas 90: Edge Protector is a must, and for less than 30k you can get a 1 AP Edge Protector. That's a must-have
LG - Landon Dickerson 91: Dickerson is the only LG in the game under 50k that can get AP Discounts (If you don't power up Randall McDaniel). That said, he gets Post Up for 1 AP and Secure Protector for 1 AP. Both are viable options to run for different reasons.
C - Creed Humphrey 90: Humphrey is the only center under 50k (at about 28k) that gets Secure Protector for 1 AP. As an alternate option (say you have Secure protector on both of your guards), you could run Identifier for 1 AP. Identifier lets you see who your opponent is usering, giving you an edge when game planning.
RG - Tevin Jenkins 92: Jenkins is the only RG under the 50k budget (48k) that gets discounted AP. He gets 1 AP Post up or 2 AP Secure Protector. Not idea, but you can make it work.
RT - Tristain Wirfs 90: Read above (Andrew Thomas).
I'll make it into a lineup and link it at the end, once I do the defensive budget beasts.