If the semigloss is not that glossy anymore, just topcoat with a good "paint and primer in one". If it is very glossy, a primer like Zinsser 123 requires no sanding. Primers do need to cure for a few days, though they can be top coated in about an hour - read directions on the can. Before fully cured, they can scratch, so don't try to test the hardness just after painting.

I recently repainted my whole house and used eggshell rather than flat. Easier to clean.

I'd clean first with TSP. Give them a quick sanding, wipe down, then paint.