More than once I've been in late night discussions around a fire or in deer camp were the topic was exactly what the OP asked or along the lines of 'if you could only keep one gun and why'. We usually had a beer in hand and were always more interested in the story behind the choice because it was all being asked in a hypothetical fashion anyways. And even if somebody was dead serious about actually being buried with a gun (and a friend or two stated they were) none of us found it odd. They said why the gun meant something to them and we seemed to understand. We never got too deep into the philosophy along the lines of 'a waste of a good gun' etc.
I'm planning on being cremated and having my ashes scattered on my wife's great grandparents ancestral homestead north of 'The Highline' in eastern Montana. Kids have explicit instructions to mix mine, the wife's and our Jack Russell /Blue Heelers ashes before doing that.
But back to the OP's question. "IF" I was to be buried with a gun it would be a stainless, birds-head grip Ruger Single 6 in .32 H&R mag. Back in 2003 I was sitting in my commanders office (ex-Marine aviator, flew combat missions in Vietnam and on one brought back a crippled F4). After Vietnam he had a break in service, went to school and received a doctorate and came back to active duty after a service transfer. One of the most honorable and moral men I've ever met. I was his squadron super at the time. At the end of the day when everyone had gone home we would discuss the pressing issues that developed or shoot the breeze (sometimes about guns). He was close to retirement and during one of those end-of-day discussions tossed me an annual gun magazine catalog reviewing everything for the year. Stated he was gifting himself an M1 for his retirement (seem to remember it was in a wooden crate, maybe the Springfield Iwo Jima edition). Asked what one gun I would pick for myself for retirement. Looked through it a while and saw that Ruger. Explained I really liked the birds-head single actions (kinda rare at that time) and the caliber. Tossed the mag back and thought nothing more of it. Wasn't planning on retiring for 3 more years.
At his retirement a few months later we presented him with the traditional military gifts. He was very appreciative and explained that it was his philosophy the retiree should be the one giving gifts to the people that got them to the point were they could retire. He passed out numerous gifts and eventually called me up, handed me a small gift-wrapped box and paraphrasing somewhat "You're the very last of a long line of SNCO's that got me here, so I guess this belongs to you. Open it when you get home". It was that Ruger.
If the colonel called tonight and said he needed me tomorrow at 0500hrs barefoot, wearing nothing but a kilt and playing bagpipes to lead the unit across freshly broken bottle shards through the front gate of Hell itself I'd be 30 minutes early to ensure the formation is dressed and covered before he got there.