3/8 barbs. If you wanted to try your stretching concept, 7/16".
I've always used matching ID tubing and barbs with clamps or good zip ties and not had issues. I know a lot of people like the 1-step smaller tubing concept and I've been thinking of trying it just to see. If you go this route, use very hot water, dip the tubing ends to heat and slide over. As they cool, they should fit very tightly.
I've also noticed that matching tubing size (say, 1/2"ID tubing and 1/2"ID barbs) nylon barbs fit much more tightly with tubing, metal barbs have a little less snug fit. It's a good idea to use clamps of some kind with barbs, especially as a beginner.