You didn't say quite enough about your Martin A to get very specific opinions. Is it a carved top, f hole model, or the more common, delightful, flat/cant top oval hole kind?
I have some opinions based on rather limited playing and owning similar instruments.
Use light strings on the oval hole A model flat tops, 10-36 or so. they were not made for todays typical strings which run 11-40 or so. Personally I like DR lights.
Most folks play mandolin with fairly thick picks compared to guitar players, and rounded points, my favorite being the 1.5mm Wegens. Many players may chime in and disagree, but that's my impression from reading many posts.
Tone guards and arm rests- can't help you there. I don't use them, and find I can get good tone if I position the mandolin to get it- keeping it away from me while sitting. most OT players are sitter downers so we can do that.
I think the old Martin flat tops, cant tops, whatever you want to call them, are great instruments. The short scale makes them easier to play, and the tone is great for anything but bluegrass. I have an SS Stewart all koa model, made by Martin most likely, that's a pleasure to play.
Be yourself, everyone else is taken.
Favorite Mandolin of the week: 2013 Collings MF Gloss top.