Arriving Hong Kong airport at 1pm, how do I take express to YMCA Salisbury? Is luggage a problem?

Well, you can take airport express to Tsing Yi Station first. Then take Tung Chung Line to Nam Cheong Station and transfer to West Rail Line to East Tsim Sha Tsui Station, Exit N5. The whole way takes around 50 mins. And the ticket fare is 60 HKD per adult.
After that, walk west around 550 yards.
Don't worry about your luggage. There are enough space in the airport express that can put your luggage. :-)