Forget the crap about having to go to R8 taper, I used morse taper tooling in my mill for many years before buying one with R8 fitting.
R8 does have it’s advantages, but when starting out, that is the least of your money spending worries.
The only problem you have is at the moment you do not understand that to use any morse taper tooling in your mill, the morse taper has to have a threaded end so that you use a drawbar to hold the tooling in position. Morse taper tooling with a tang is really only designed only for use in either a drilling machine or in your lathe tailstock.
There is also another catch as well, some MT tapers can have different threads (usually two different ones) in the end, so make sure you always buy tooling with the correct thread, or do as I did, have two drawbars so that I could fit either type. As suggested, a length of threaded rod on a smallish machine will be just fine for the second drawbar.
Just on a safety note side.
You should not use drill chucks for holding milling cutters except in very light loading processes,
Drills actually have a soft shank and can be held with the hardened drill chuck jaws, but because you are trying to hold a very hard milling cutter shank with hardened drill chuck jaws, the cutter is liable to slip or become loose and so at the very least, ruin your job, but it could end up a lot worse.
You really need to save your pennies up and buy say an ER collet chuck for holding cutters in your mill, or do as I do (costs about the same price) use dedicated spindle collet sets, they tend to give you a little more throat clearance, but are not quite as versatile as the ER series for holding different sizes..
I hope this explains it a little better.
John