Tex - I don't know all the answers, as I'm not 28 yet, but I'll take a stab at a few:
1) The only guaranteed way to get a better gun is to pick a faction and level it to 3. I'm doing Vanguard right now because I already leveled them and FWC to 2 for the armor I wanted, and I like Vanguard's weapons selection better. One level of rep takes me about one week of play.
The other way to get a legendary or better (in this case, Exotic) gun without it being a random drop is from Xur, but he randomly brings any Exotic weapon in the game, so he's not very reliable. The last two have been Primary weapons, but the first one was a rocket launcher. For a reliable legendary, see the faction vendors.
2) Nearly everyone says 27 is fine for the raid, though I've never done it or the Nightfall. Hoping to try both this week (I'm 27 now).
3) The first Public Event you do every day gives you some kind of rare material, which can be a shard. The Daily Heroic Story Mission guarantees 1 or 2 Ascendant materials if you do the higher difficulites, so that's either Shards or Energy. I co-oped the Daily at level 28 difficulty last week, and we were both level 27. It was hectic and a challenge, but we did it.
After that, you can occasionally get a shard in many random ways, but the reliable source is to disassemble legendary armor. I will probably start using my Marks to buy equipment to shard after I buy my Legendary Auto-Rifle, although a case could be made that I should wait until I buy some other legendary special weapons, too. The issue here is that your level matters more than most anything else for effectiveness in high-level content, so getting to 28 seems more important than upgrading one of my three (elements, natch) Fusion Rifles from Rare to Legendary.
Just my thoughts, higher level players may have more insight than I do.
EDIT: And some of them are faster typists than I am, too.
