Breaker/Junction Box
1” conduit has plenty of room for four #6 copper THHN. Although the ground can be #8.
1” conduit also has room for three #4 aluminum XHHW and a #6 aluminum XHHW ground, if you’d like to save some coin.  The lugs are aluminum, do why create a dissimilar metal problem?
Your #6 copper or #4 aluminum may be breakered at 70A, hence my reco for that size of ground.
Having a little kitchen is like being a little pregnant, when it comes to number of circuits required!  You still need two  dedicated circuits for kitchen counter receptacles. The oven needs a dedicated circuit.  Disposal. Dishwasher. Built in microwave. Etc. The bathroom needs a dedicated circuit.  Laundry room etc. We are going through panel spaces very fast!
As such the spa panel will not cut it and you’ll want gosh, at least a 20 space... but getting too few spaces is a serious blunder easily avoided,  so why short yourself... get a 30.