In reply to Phil1919:
It's sort of my commute, ish. I ride from the Manchester Velodrome out to New Mills. Sometimes I go via Reddish Country Park if I'm feeling meandery.
Personally, what I'd do, provided it's at a time of day when the canal tow path isn't going to be inhabited by weirdly menacing teenagers is from Piccadilly Station head north, get onto the Ashton Canal towpath and ride past the velodrome. Look out for a sign on the right to pick up Route 60 - the Fallowfield Loop. Follow that entirely off road, entirely do-able on a road bike if you felt like it, until you join the Route 6 just before it goes into the Country Park.
Your planned route does work, kind of, but it mixes you up with traffic and some of the signage is a bit misleading. I tried it a couple of times but ended up relying on googlemaps on the phone to get me to my destination.
From the country park route 62 is a wiggly wriggly route, and I've never had much success with following it on signage alone. If you check out www.cyclestreets.net and plonk start and finish destinations into some kind of GPS device that works better. If you don't have such a thing available ... take a map!!!
Post edited at 16:54