Perfectly possible to use a normal domestic vacuum cleaner, but it will fill up VERY quickly. A better bet is the larger capacity wet and dry drum type, although again, capacity is the limiting factor unless you go in for an additional drum before the cleaner.
Since both circular saws and routers make relatively fine dust or small chips, hose diameter isn't that critical, so the existing one is likely to be OK.
Oh, yes, and welcome to the forum.