I agree with the previous poster, take the train to Centraal. Given your arrival time, I'd probably suggest staying near the train station for two reasons...1) check in, drop off your bag, and you have a little time to walk toward Jordaan for a beer or whatever you're interested in...2) leave your bag at the hotel the next day instead of dragging it around on a tram or while walking, and then pick it up on the way back to the train station. Canal tours also leave near there too if you're interested. It's personal preference, but I find the Leidesplein a little touristy and try to avoid meals there.
I've stayed at the Renaissance a couple times, which is an easy stroll with luggage from the station, but there are other options nearby too.
Unfortunately, while I'm a bit of a foodie myself, I tend to go light on lunches, so can't help much there. Amsterdam isn't really a foodie city in my opinion.
I'll be in Amsterdam for about 36 hours in 2 weeks, and having done many of the tourist things, this thread caught my eye. Hopefully you'll get some more lunch recs I can use as well!