Very familiar with the area you are talking about. There is a sustrans route all the way from the centre of Glasgow to Port Glasgow. Are you arriving in Glasgow by train? Just come out the front of central station, turn right and right again heading south to the River Clyde. The cycle route starts on the Broomielaw, heading west to the new "squinty" bridge. Cross the bridge then go past the new BBC building and into Govan. Route then crosses the M8 motorway by way of a footbridge, then to Pollock park, round Linthaugh road in Pollock to Ross Hall hospital, then through part of Paisley to Paisley canal station. From there it is simple: follow disused railway line, now tarmac path, all the way (apart from a short road section in Elderslie)to just short of Johnstone where you go right (still on disused railway line), through Bridge of Weir, Kilmacolm and then onwards to bandit country (Port Glasgow

). The track ends at the top of Port Glasgow (Montrose Avenue area) but the sustrans route continues to Gourock.
I have used the route several times and never had any hassle. Occasional areas where the local wine experts like to sample their goods and the resultant broken glass on the track. Don't forget your waterproofs

!