Parts finder for an online car parts shop

Your online shop sells car parts to drivers and small garages, and it lists 2 million parts. A shopper first picks their car: make, model, year and engine, from about 30,000 versions. They then pick a category, such as brake pads, and see only the parts that fit their car. They can filter by brand and price, and sort by price.

Suppliers send data on which car versions each part fits, and it is loaded every night. A part fits 40 car versions on average. Some parts, such as wiper blades and bulbs, fit over 5,000.

The shop gets up to 50 searches a second, and results should appear within 300 ms. A part must never be shown as fitting a car it does not fit.

What do you store about which parts fit which cars, and how does a search for brake pads run?