DO NOT GET A DRILL PRESS TO DO ANY MILLING.
You appear to be inexperienced in machining and using a drill press to carry out milling operations is a disaster waiting to happen, even for "experienced machinists".
A post-type vertical milling machine is an inexpensive way to start milling operations.
A rotary table allows the work mounted to it to be rotated past a cutter, or used for positioning such as drilling holes on a bolt circle.
The rotary table is usually worm gear driven at crank-to-table ratios varying from 40:1 to 90:1, with 60:1 and 72:1 other common ratios.
By fixing the work piece to the rotary table top you can machine the outside and inside diameters of thin disks in one set-up provided that the remaining ring is fastened to the rotary table top. Here cleverness in workholding pays off in spades and $$$$$! One way is to use finger clamps and transfer these from the inside of the ring to the outside after milling the outside diameter.
Because of the worm gear reduction it can get tedious turning the crank (hand wheel) to rotate the work past the milling cutter hence the advice to add motor drive to it. A variable speed electric hand drill would suffice if you don't mind the noise. Again inventiveness is the key to a low-cost solution here.
With clever fixturing you can finish the entire ring with one set-up on the mill! For example you could bolt a piece of MDF onto the rotary table and glue the work piece to this for the polishing operation. If you glue the work piece from the start then for the milling operations finger clamps or wood screws would still be required for additional strength to resist milling forces.