Agreed.
I don't know the whole route, but the bits near me are canal towpath and disused railway line, so are flat and sandy/gravel.
I wouldn't use my carbon racebike, as when wet it all turns into grinding paste, but it's certainly not offroad enough to need a full-suspension MTB and a hybrid with 28-35 tyres will be fine.
At that price, buying secondhand - just get something which is sound and you'll be fine.