What heroes/roles to play to increase solo MMR?

I'm primarily a support player who just switched over to rank, still stuck around 1k. There have been occasions when I get absolute noob carries who can't really farm and take teamfights well, and when I go for a more offensive role the feeders in my team make it difficult to win the game.
I know that it doesn't happen all the time - the enemy team will have dumb players too, sometimes I'll have a good carry on my team, etc. but I want to know if there's a more consistent way to ensure winning streaks.

I guess I should learn heroes that can fulfill a variety of roles? Or something that can start out as a support and transition into a semi-carry (if such a hero exists)?

It's not the role that matters, just pick heroes that have high impact heroes like Earthshaker or Disruptor if you like playing support.

Well, to effectively increase your mmr you may spam only one hero and win. Pub players often do this. It is effective, but veeery boring.

As Wulfstan said, you may pick supports with big impact.
You want supports that can transition into semi-carry?
Crystal Maiden is very good example. Buy Glimmer Cape, go into their team, ult, glimmer cape. Your teammates should do a follow up. 1k players never buy dust so it will be easy for you(they even forget about BKB sometimes).

Another little question - how good is Naga Siren? From what I can tell, she is viable at any position (1-5) so depending on my teammates I can go support or hard carry, while sticking to one hero and getting good with it.
But then, is it right to call Naga noob-friendly? If yes, what are the main skills required to use her effectively?

Naga is NOT a noob-friendly Hero, especially carry naga. Her low, low base damage and mediocre attack animation makes last-hitting difficult and even once you do get Radiance you need to be quick with your micromanagement to make the most of the item. You also need good map awareness and judgement as to whether you can stay and push the tower that bit longer.

Thanks Terathiel.
On a similar note, what about Beastmaster? I can go almost any lane if I get a favourable matchup. (Counter-)Pushing capabilities are also pretty nice, and he has imo one of the more easier micromanagement requirements in the game out of any minion-summoning hero. However, I don't think he snowballs very hard into the late game as a semi-carry (at least not without appropriate items).

Thoughts?

Beastmaster?..... I'm going to have to say that is conditional.see, Beastmaster is a hero that can't kill solo reliably past the 15-ish minute mark, even before that it's shaky.

But give him one another hero with him, and he becomes a ganker second to none, with his slow and dps increase as well as the muh****in' roar.

Windranger is very noob-friendly.

You can do stuff early game, come back from behind, and destroy noobs late game 'cus they don't buy BKB (to block Maelstrom) or MKB (for Windrun)

If you look at my support Naga Siren thread in the theorycrafting section, that might be a viable option. You just pick up like 3 clarities and a smoke in your starting items, hit level 2 or 3, then start roaming.

I wouldnt consider naga and wind very noob friendly.
But honestly i encourage people to play heroes they enjoy, you are usually better if you are having fun playing a certain hero.
I mean i started with timbersaw, clockwerk, sand king and rubick, not the easiest heroes really, but i had fun with them so i did well.