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Will that work together?
You may have an issue with 8-speed chain not fitting between 10-speed sprockets, and conversely if you switch to 10-speed chain it might not play nicely with 8-speed sprockets. If it's a beater wheel you're not going to use for anything else, a singlespeed conversion (e.g. https://www.tartybikes.co.uk/single_speed_kits/trialtech_single_speed_spacer_kit/c511p10341.html + https://www.tartybikes.co.uk/splined_sprockets/gusset_1er_sprocket/c28p418.html) might be the best plan. I can recommend trainer specific tyres, I use the Conti but I doubt that the Tacx or Vittoria options are much different.
So I want to get a turbo trainer. The bike I'd use it on has an 8-speed campag groupset with a nice wheel on it, I have a cheap wheel with a 10-speed shimano freehub on it that I could chuck an old tyre on. Will that work together? Obviously not going to be changing gear, the chain just needs to sit on one cog and spin the wheel as I pedal and not skip or fuck the chain up.