I am on a pre 1985 nikishi custom sport, i'm upgrading, willing to spend some money, not too much.

The chain is slipping, i am not to bike savy. 12 speed. I have it on the smaller crank on the peddle crank but on the crank on the rear tire i move it all the way to the top crank. I assume lower gear ratio
(i am somewhat car savy lol) On the rear crank it will slip from the top crank to the middle crank, which is the 3rd crank from the top or bottom, however you wish to look at it

What is the problem and solution. ( not too expensive but i am willing to pay a fair amount)