So, there are some different levels/kind of keyboard that may be more "ergonomic" than a traditional one. Howe weird are you looking to get?

Re: budget, ergo boards tend to be low-cost DIY kits, but you generally have to do a fair bit of soldering. You can also get prebuilts, but they're not super cheap since it's not like, assembly line production in most cases, it's one person building it by hand. There are some exceptions that are more production, but they won't be as cheap apart form like a Keyboardio Atreus or a Planck or Preonic

Alice layout: Normie layout "unisplit" with a slight split and angle on it. Will be easy to adjust to, minimal ergonomic difference from regular board. But having split spacebar is a big win in itself to be honest.
Regular board, but split, such as a Quefrency or Sinc from Keebio. Layout isn't ergonomic for your fingers, but you can put them at whatever angle suits your wrist, and you can tent them as well (angle the halves)
Basic ortholinear. All keys are in a grid, like Planck, Preonic, XD75, MechWild Waka. Layout is arguably a bit more ergonomic than regular, will require more adjustment. Many of these boards are not split, although some are.
Columnar stagger: Each column is a different height, reflecting the different lengths of your fingers. More ergonomic. Mostly split boards like Corne, Kyria, Sofle, Lily, Iris, Ergodox, Moonlander, with some unisplit boards like Reviung and Atreus. You can use this tool to compare layouts
Keywell/Dactyl: Keys are positioned in a bowl like shape, three-dimensionally. Examples Dactyl, Kinesis Advantage, MoErgo Glove. These will be a lot more expensive if you want someone else to build them for you.

There are tons of different options out there, so you'll wan to start by narrowing down what kind of layout you want and how DIY you want the build to be. The actual builds are mostly pretty straightforward, but most ergo kits do require you to solder diodes and controllers, not just switches. And some of the more esoteric ones have a higher difficulty level, like the keywell boards.

Ortho and columnar stagger boards will take time to learn to type on at speed. Many users also take the opportunity to learn a new non-qwerty layout at the same time since they need to build new muscle memory anyway.

You'll want to pay attention to the layouts when you are picking keycaps. Many ergo boards use all 1u, or 1u plus a couple of spacebars. However, others use ergodox-style layouts with several keys of other sizes. Kitting can be difficult if you want all your keycaps to correspond exactly to what you have those keys assigned to do. Life will be easier if you are a touch typist and willing to make use of blanks or novelties.

This is a really great resource, but just wanted to add my 2c. I've had (or at least used) most of the variations on this list, and if I could do it again, I'd probably just further down the list faster. I'm a programmer by trade so I spend a lot of my time typing, and I can't express how much of a positive impact building a dactyl manuform has had on my wrists (and just general typing comfort). If you have a 3D printer already it's actually pretty easy to put everything together, and you could probably definitely do it all yourself under your budget (so long as you already have the soldering equipment). The kits are definitely going to run you more though. That said, in my opinion, its worth going at least to columnar stagger if you're going to go down this route! (Plus - if you're already relearning to type, do yourself a favour and switch from qwerty to dvorak or colemak or something like that!)