Run 8/3 Romex in conduit. On you main feeding your sub put a 40 amp breaker. Your sub can be a 100 amp no problem cause your feeding it with a 40 so it’s technically a 40. If you wanted to do it cheap buy 12/3 run it on a split 20 and that will do what you need at 1/4 the cost. No sub panel needed just run direct to plugs and lights but get 20 amp plugs and switches