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Kind of ties in with Airtime's question but there are 2 trendy options I've heard of, one I've used and the other I've only had recommended.
Bushboard is a laminate which has a quality finish and the laminate is a few mm deep so it can be routed for recessed sinks etc. It's nice stuff, good to work with and forgiving on joints where you can fill and polish it unlike normal laminate.
The other is Richlite which is very architect friendly, it works very much like hardwood/board but looks contemporary design etc. etc. I've not used it.
Best option for cheap kitchen worktops in wood is Beech. It's chemically neutral (or something like that), Durable and reasonably priced in the thinner versions, I think Ikea do it by the sheet.
For laminate worktops there are one or two stand out brands, Formica being one of them. The quality of chipboard/density and thickness of the laminate are defining qualities. I usually go to a laminate worktop specialist and choose on price depending on the job. These days most of the kitten work I do is high end so the worktops are someone else's problem.
It's not just the templating that costs the money, it's the material and what has to be done to it to shape it for your kitchen. Marble/Granite is great if you're not OCD, otherwise you'll be polishing it the whole time, especially if it's black.
These stones are also porous so you can bleach them with some oven cleaning products and stain them with oil. Personally I wouldn't have quartz, to me it lacks the personality of a natural stone. There's a huge warehouse in Battersea called MGLW that has massive amounts of stone, you can buy a sheet and then instruct a mason to make it up. The stone they have there is incredible, they have a website with pics but it doesn't beat a visit.
You can template it yourself if you want. Just remove your current worktops and cut 3mm hardboard to exactly the same size. If you want different shapes/overhangs then cut 3mm hardboard to the shapes. Mark your sink position and give it to the stone mason. If you screw up they will charge you or worse you'll have ruined the material, but generally if you're a couple of mm out on the template you can chase the wall a bit.