For the interior carpet, use a stiff handheld dust broom in one hand and your vacuum in the other. Use the brush to loosen any ground in dirt, and the vacuum to suck the dirt up. You can follow that up with shampooing if needed, but you'll get a much better result by starting with just a vacuum and substantial manual agitation of the carpet fibers.
When you shampoo, make sure that you completely rinse the shampoo out of your carpets before drying, otherwise your carpets become a rag with cleaner for your shoes and will get dirty more quickly than before.
For crevices they sell brushes in the auto detailing aisle at the store with long and soft bristles, grab one of those and go over all seams with that while following along with your shop vac. Follow that up with a wipedown with a moistened microfiber towel, then another pass with the crevice brush, then wipe down with protectant. I like 303 Aerospace protectant and a whole host of specialist products that I have from when I did this as a side gig, but the standard Armor-All is just fine as long as you make sure to buff it to a dull sheen after application. If you leave it oily shiny it will attract dust like nobody's business.
99% of the result is in the cleaning, so focus on that before worrying too much about dressings/polishes/etc.