You're asking about Capilano Suspension Bridge, which is handy to know if you get lost and are struggling to find it.
In terms of the luggage, that will depend on you, as will food time.
From the airport, you'd get the Canada line (the only option) sky train in to Waterfront (the end of the line). As you leave the station, you'll see the sea-bus terminal. Hop onto a seabus (boat) across to the other side (they only go to one place). At the other side, walk out quickly and into the bus area, and look for the bus to Grouse Mountain. It also stops at Capilano Suspension Bridge.
Coming back, you can repeat this in reverse, looking for a bus to Lonsdale Quay, then the seabus over to Waterfront, noting on your right that you'll see the big Stanley Park. Decide now if you want to walk there. If so, that's easy. If not, get out at Waterfront and walk up Granville until you hit W Georgia. Busses heading to the right will be going to Stanley Park.
Depending on the bus, some will go through the park and over the bridge. A nicer option is to get off at Stanley Park and walk right around the entire park, which will give you a great view of the city, the Lions Gate bridge and the park. (Note, the bridge is on the far side of the park to the city). It's about a 12km walk to do the full circuit though, so be prepared if you're considering this.
Bonus tip: If you have Google Maps and a smartphone, as you exit the Waterfront station you'll see a Starbucks, as well as at Lonsdale Quay. There's also one at W Georgia and Granville (well, two), and one near Stanley Park. They have free wifi, which is handy for checking bus times on google maps, and your flight updates. There's also free wifi at the airport.