For CD player, CDs, and the associated mechanisms.... rather simple tooling is required.
A good tool kit (similar to PC repair kits), compressed air, detailers brush, good unused CDs, magnifying glass, and I have found jewelers tools to be handy. Also there is a silicon lube that used to be available for small gearing, like clocks. I have found this to be excellent!
Beyond that, the "know how" is probably most important. Just using the "You-Tube" tutorials, I have learned to repair most CD players. Where skipping, non play, and improper loading is concerned, most fixes are minor. Up two levels,... and it may not be worth it. Laser repair or replacement beyond cleaning the lens..... problematic and replacement parts sometimes .... elusive
I would recommend you do your first repair on a unit... you don't really like. Why? Not knowing the proper handling and approach can destroy a good player. So.. go with an experimental.... besides, practice makes perfect!
Also... and interestingly, I have found most CD players of excellent recovery value, did not or were not working due to a stuck CD... ?! Most persons not "troubleshoot competent" will ditch a perfectly good player, if and when the CD gets stuck. Believe or not, the fix is to remove the chassis cover and recover the disc

I have two excellent players relieved of this malfunction... and these are a quality Panasonic and SONY.
In similar ways, the recovery for DVD is the same.. as for SACD.. have yet to get one.