What is the best 3D printer for under 200 USD?

Well, $200USD is not much to play with ... you're probably going to have to compensate a bit by tweaking and upgrading as you need. The Ender 3 Pro is often recommended as it's rather "open" in design and has many customisations - but it's effort and tweaking that you need to have the time to put in. Others get entirely frustrated and claim it to be the "worst" experience in ironing out prints that don't come out straight (because of incorrect assembly) or problems with under-extrusion (due to damaged/worn parts), etc. If you want it to just work for a more commercial purpose, you're probably looking to spend at least 20x as much ...

Carbon fibre-based filament is a difficult thing to print. It's going to need a hardy nozzle - the brass stuff that's normal for low-price printers is going to wear out, so stainless steel or better is recommended. That in itself is not a massive expense but it is a little hassle. The next issue is that you need to get your bed to about 80c, which open printers like the Ender 3 Pro may not be able to maintain especially in a room with some airflow going - so building a "hood" or "box" around the printer to retain the heat is highly recommended. Add to this that you also need a print temperature of about 250c or so means that you're probably pushing the upper limit of the cheaper printer's all-metal hotends.

PETG is a little more forgiving of print temperature, but the bed also needs to get to about 75-90c, so again, it might be a bit of a push for the printer especially in colder climates.

Quick printing is very much dependent on a few factors - the size (volume) of the model, the complexity of the geometry is a big one. For the most part, cheap and quick definitely don't go together and many of the cheap designs aren't rigid enough nor well designed enough to print well at high speeds, even if it can. For example, my printer is advertised with a print rate up to 100mm/s, with a recommendation of 60mm/s. What I find is that anything above about 40mm/s causes noticeable loss of fine details because the head isn't following the path just right as the play in the belts and frame start to also induce "shimmer" or ripples in the walls. How many "days" a print takes really depends on a lot of factors - download some slicing software (e.g. Ultimaker Cura), select your intended printer, change a few settings and run your model through that to get an estimate of print times.

- Gough

Thank you for the insight. I plan to build a hood/box out of some polycarbonate I have, because I plan to print inside and have heard the fumes are bad. I also have realized that I would need a hard metal nozzle if I were to print with Carbon fiber and am willing to get that after the original purchase of the 3D printer. I was mostly hoping to find a printer that with the right modifications would be able to print those filaments in the future, so I wouldn't have to get an entirely new printer. In your opinion do you think the Ender 3 would be able to be changed do this after purchase? 

Thank you for the insight. I plan to build a hood/box out of some polycarbonate I have, because I plan to print inside and have heard the fumes are bad. I also have realized that I would need a hard metal nozzle if I were to print with Carbon fiber and am willing to get that after the original purchase of the 3D printer. I was mostly hoping to find a printer that with the right modifications would be able to print those filaments in the future, so I wouldn't have to get an entirely new printer. In your opinion do you think the Ender 3 would be able to be changed do this after purchase? 

Depending on the materials, some smell bad (ABS especially), and microplastics in the air in general are probably not good for health. So perhaps not a bad idea to put it in a box - but if the printer gets too hot, you might find the stepper drivers going into protection or the power supply overheating. So you'll have to play with what works in your climate/condition. I dedicate a room to 3D printing and vent that to the outside.

You can definitely get hardened stainless steel nozzles - they're not expensive at all. Changing it will require a bit of care - sometimes it's best to do it while the nozzle is hot because of remnant plastic in the threads which may cause you to destroy the hot end attempting to unmount the old nozzle cold. As a result, just be aware you'd be handling ~250c hot metal while doing the nozzle change.

The Ender 3 Pro may work, but for what you save on price, be prepared to have to do at least a little bit of tinkering to get it going and periodic tinkering to keep it running. Like anything mechanical, things can wear out and break. Similarly, the unit is a manual-levelling printer (as far as I know) and getting a good bed level adjustment is key to getting good first layers which often will be the thing that makes or breaks a print.

Spending more may be useful, but it's usually not just a little more - it'll be a lot more for something that's more designed for "industrial" scale printing. Those often have better mechanics (e.g. coreXY rather than "bed-slinger"), come with integrated auto bed-levelling, may have multiple extruders for mixed-material (e.g. two material or one material + support). They are often quite a bit more pricey - my home hobby printer cost about US$150 while the one I use at work cost US$8,000. Of course, the one that's at work is a lot more "set and forget" and has a wide catalogue of materials that it is set to work with.

- Gough