I recommend you buy a builder's canister vac. It's like a giant Henry, and should have a replaceable cartridge filter but be able to take huge paper bags as well (mine is 30 litres but some are bigger). It can eat nails and broken bricks as well as sawdust and plaster and insulation. It is rather noisy.
Titan brand from Screwfix is adequate and quite cheap, and they have a good returns policy if it goes wrong (if it does, get a refund, not an exchange, and buy a new one, which will have a new 2-year guarantee period). Get a pack of bags and at least one spare cartridge filter. You can brush it clean when clogged, and, eventually, wash the dust out in a bucket of water. The bag will delay clogging but can get torn by broken glass or brick. I recommend a wet and dry, which will also suck up water from a leak or a blocked drain.
Examples https://www.screwfix.com/c/auto-cleaning/wet-dry-vacuums/cat810212?brand=titan
Plaster dust is very fine and abrasive and will clog your domestic vac, and may damage the motor, so don't use it, and hide it from the builders.
When you do your post-build clean, you have to do the lampshades and bulbs, curtains and blinds, and the tops of doors and doorframes. The dust gets everywhere, including inside wardrobes and drawers. Invest in a roll of plastic garment bags from Ebay. It can damage electronic equipment like TVs and computers.