Depending on what you want to spend and what skills you don’t mind learning:
YoYoJam offers many models that have two bearings: A slim bearing pre-installed for responsive play to get started quickly, and an included wider bearing for unresponsive play once you start progressing along. Models like this include the Legacy II, Chaser, Dark Magic II and others. The Dark Magic II is a proven yoyo for beginners and advanced players alike, but is just over your $40 budget.
If you don’t mind a bit of easy to do upgrades, the YoYoJam Classic would be ideal to start with. It ships with rubber ring response and a slim bearing. It’s tug responsive in this configuration. When you start advancing and want to get into unresponsive play, you can put in a full width C-sized bearing(which you can buy as a separate item) and perhaps suitable response pads(sold separately) to replace the rubber rings. Alternately, you can use flowable silicone for the response Total cost for the Classic, a YoYoJam Speed bearing(an affordable C-sized bearing) and YYJ Silicone o-ring response pads should st you back right around $20. For a few dollars more, you can get the Legacy II, which includes both bearings and the response is already the pads. I think the Classic is a bit better shape.
If you want a yoyo that can as-is go from responsive to unresponsive, you want the YoYoFactory Velocity. You can use the dials to make the response system move in or out(per side). The yoyo can go from way too responsive to dead unresponsive and anything in between. No extra parts are required. It is a touch on the light side.
I recommend against clutch/brain/auto-return type yoyos. After you get your thow down, they become rather pointless. If you’re a little kid, then sure. If you’re older than 8, maybe not such a good idea.
OK, onto your other questions:
Anodizing and polishing require metal yoyos. The good news is you want to screw around with this and you can purchase very low cost metal yoyos to experiment with. The best part is these aren’t junkers either!
Anodizing involves dyes, acid and electricity and is a somewhat dangerous process that takes a lot of skill and practice to be god at. If you can, please learn to do this from someone else. There are tutorials on the topic. Whether you choose to market your skills and/or work to others I could care less about. However, if you get good at it, why not? Sure, do some for fun, but if you’re doing a good job, why not see about offering to anodize yoyos?
With painting, you’re using usually an automotive grade paint and an airbrush to apply. What I dislike about paint is that it will flake and chip over time. That’s just how paint is. Another option is powder coat.
Polishing a yoyo involves removing the anodizing(if need be). This can be as simple as a sanding process, or as complex as using caustic chemicals(oven cleaner is a popular one) to strip the anodizing. Once the anodizing is removed, you use progressively finer grits of sandpaper to make the sanding marks smaller and smaller. Many use wet sanding methods. After a certain level, you would then use a metal polish to remove the last scratches and bring it to a mirror polish.
Have fun. I play for recreational purposes only.
i would love to custom paint/anoxidize some metal yoyos and show you guys my works 
Im 16 and I use to own a Blue Dark Magic 2 but unfortunate circumstances happened and it is no longer in my posession ( it was stolen). Ive currently been looking into a YYF Velocity (new). Its cheap and i can easily swap between responsive and unresponsive play.