Was getting new machine because I am fed up with beach balls. Will an Apple store do these upgrades or should I find a private repair shop? Is it that hard to do these upgrades. I know I am all over the place, that speaks to my ignorance. Thanks for your patience.
I strongly suspect that upgrading the RAM in your older mini would be a waste of money. While having too little RAM in a Mac that is being asked to do a lot of heavy lifting, such as 3D graphics, or video editing, or running six or seven major apps at the same time, might cause a bit of beachballing while it did a virtual memory swap, it wouldn't normally cause such a persistent beachball problem that you would become "fed up."
I have in my office a 9-year old iMac with only 4GB of RAM installed. I use it to run a couple of legacy programs that no longer exist for the Mac. that require OS X 10.6 (because OS X 10.6 was the last version of OS X that included Rosetta). I also dual-boot this machine into El Capitan. Running either Snow Leopard or El Capitan, this iMac has excellent performance, and I never see a spinning beachball, despite the fact that it only has 4GB of RAM installed.
You state that your mini has a 2.5 GHz i5 processor. That means that your mini is what...only about 4 years old? That's too new a Macintosh for you to have to purchase an entirely new one.
I'm willing to bet that your older mini's beachball problem could be easily resolved, and that it can regain its like-new performance, but you have to work with us a bit. Did you have a look at the Web site I suggested?
Macintosh OS X Beachballs!
http://www.macattorney.com/rbb.html
Did you try the things suggested there? If you got hung up with any of the suggestions, please tell us which one, and what about it confused you, and we will try to help.
Of course, if you don't want to deal with this problem on your own, if you have a brick and mortar Apple Store nearby and make an appointment, they will do a diagnostic on your mini for free that will only take a minute or two. You don't need to be covered by AppleCare for them to run a quick diagnostic on your computer, and then at least you will know exactly what's wrong with it.