This is a very common problem, but 5e =/= D&D. The core rules (take a number, add it to a d20 roll, compare to another number, get effects based on whether it is higher or lower, and maybe by how much higher or lower it is) don't have to support D&D-alikes, but can be used as a base for a lot of games.You're running to the issue real quick that modern DND has almost zero consideration for feature cost logic and is more focused on troupe/character concepts than balanced.
It's doable but by the time you're done it would not look anything like 5e.
That's pretty close to how I'm doing my classless 5e game. 3 feats at level 1, then 1 feat every level past that. No extra attack, but you can get feats at level 5+ that approximate it, depending on your concept.For a low magic adventure we can use what a call the Thug template Base on the NpC in the MM.
point buy 25.
choose a good and a bad save.
choose 2 skills.
hit dice d8
proficient in light armor and simple weapon.
gain a feat at level 1,2,3,5,6,7. That must be a feat!
Gain usual ASI at level 4.
Gain extra attack at level 5.
Thug don’t gain level past 7!

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.