Well, you need a tank. The cheapest tank would be 
Nunu & Willump, but he is definitely not the best tank because he has no hard cc or taunts. He's still rather obnoxious and hard to kill though! If you're willing to bust 3150 I'd get Shen, he's amazing in basically every situation, and REALLY fun!
A support character would be good to have on the team. Soraka is the cheapest at 450, I think Zilean's super fun (1350) but Janna is probably the support that is best in more situations, and would really compliment your Yi well, she is 1350 also.
So after these additions you only have one damage dealer that's dealing physical damage, so I would get another physical damage hero. Preferably one with CC. If you're going with Ryze you can get a squishier hero, but if you're going with annie you're going to want a tanky dps. Tanky dps are good in both situations, so I will suggest tanky dps characters. Nasus would be good and he only costs 1350, but his only cc is a slow. He is still fun and can deal a lot of damage. However Xin Zhao I think would be better because he has better cc / initiate, but he costs 3150.
So Master Yi (carry), Annie/ Ryze (cc/mage/ offtank for ryze), Janna (or Soraka/Zilean), Nunu & Willump for tank (or Shen if you're willing to spend the IP), and Nasus (or Xin Zhao)
Nunu & Willump, but he is definitely not the best tank because he has no hard cc or taunts. He's still rather obnoxious and hard to kill though! If you're willing to bust 3150 I'd get Shen, he's amazing in basically every situation, and REALLY fun!A support character would be good to have on the team.
Soraka is the cheapest at 450, I think Zilean's super fun (1350) but Janna is probably the support that is best in more situations, and would really compliment your Yi well, she is 1350 also.So after these additions you only have one damage dealer that's dealing physical damage, so I would get another physical damage hero. Preferably one with CC. If you're going with Ryze you can get a squishier hero, but if you're going with annie you're going to want a tanky dps. Tanky dps are good in both situations, so I will suggest tanky dps characters.
Nasus would be good and he only costs 1350, but his only cc is a slow. He is still fun and can deal a lot of damage. However Xin Zhao I think would be better because he has better cc / initiate, but he costs 3150.So
Master Yi (carry), Annie/ Ryze (cc/mage/ offtank for ryze), Janna (or Soraka/Zilean), Nunu & Willump for tank (or Shen if you're willing to spend the IP), and Nasus (or Xin Zhao)
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I've posted here the last few weeks since I started playing. I have finally convinced 4 of my friends to play with me, and we wanna come up with a team that we can play as together while we learn to max our effectiveness. The two champs I have really played are Yi and Veigar. One of my friends really wants to play Yi, and one wants to play Annie or Ryze, which I kind of figure means I shouldn't play Veigar. So basically, we have 3 spots left to fill in addition to Annie and Yi. Could anyone recommend a team you think would work well? Ideally, it would be low IP characters, (450 or 1350) but if you really think a char could be especially useful, I would be willing to learn a more complex character. Thanks so much, sorry if it's a vague question! If you have any questions, just post and I'll respond very quickly! Thanks!!