I don't print asa so won't be able to tell you which printer is good but don't forget that asa release fume and substances dangerous for health, better have a place design for it with exhaust and all the necessaries.

https://chinacolours.com/is-asa-filament-toxic/

https://help.prusa3d.com/article/asa_1809

I have a qidi Q1 which I'm using to print ABS parts for a new Voron right now. It's working very easily even on default settings, although I haven't made anything big yet, and I don't know if ASA is harder to print.

As much as I lobe the Prusa Core One I have at work, it doesn't seem to be the best for ASA. I printed a few very large flat parts in ASA a while ago. Heating up the chamber takes forever, and warping / adhesion issues happen a lot on default settings, even with their own brand.

My Creality K1 does a decent job with ASA. You will either need to vent it outside or put some carbon filters in it to deal with the ASA fumes though.

I have printed ASA on my Anycubic S1. It's enclosed but doesn't have an active chamber heater. It uses the bed heater to slowly heat the chamber. It's $350.

It technically worked the very first time but it still took like 3 prints tuning the temperature to get good layer adhesion. (I was printing extremely thin and narrow parts and the ASA would break along layer lines.)

Going only by YouTube reviewers, the Qidi Plus 4 seems to be the best low end for "engineering" filaments. $700 and out of the box it has a hardened nozzle, high temp hardened extruder, and active chamber heating- plus a 305mm build volume. Even their $400 Q2 has a hardened nozzle and active chamber heating.

You’re gonna get some pushback from the open source people (and to some degree, I am one of them), but frankly the Bambu Labs printers are so goddamned easy and reliable you’d be a fool not to consider them.

I think most printers can handle ASA as my anet a8 managed it. Personally I would look for used prusa's in my area they are like 500€ and I think they would be good enough. BambuLab printers are also great but I am not a huge fan of companies that turn off features that were offered previously like making all their stuff proprietary, so when you want to connect a slicer to the printer you need to go into a separate mode or something like that, I haven't owned a BambuLab.