So I do a 
top and I like suggestions in dealing with champs that have massive sustain like 
and 
or dealing with ranged champs like 
, 
or dealing with 
. (Btw I know that is a jungle better but he's the reason I started to play leauge and I don't like to do jg).
Hecarim is actually great in 3 different sections. Top, Mid, and Jungle. When it comes to Tryndamere, items such as Thornmail helps out quite a bit, as well as taking ignite for when he uses his ultimate. Same thing for Aatrox with his passive. Tryndamere can get aggravating versus AD with his BAWKBAWK! chicken ability, reducing a lot of AD from opponents with it. Making great use of Homeguards helps you with getting back to lane fast after a shop or heal, and is devastating with Teleport. Use that combination in teamfights to dispose of their bottom lane ADC, or their midlane via a flank. Just make sure that your team actually helps with wards to set these things up. I would say that your starting item would be the Crystalline Flask for extra sustain, or boots and potions. If you run a toplane Smite, ask your jungler if you can snag the Gromp buff, and build towards Challenging Smite with Cinderhulk. That with Thornmail, gives you a better boost for trading with him. You can also level up your AoE heal heavily for sustain and trades.
Against Malphite, probably the flask for sustain, and make sure you play carefully. I haven't fought against Jayce yet. Teemo...again, use sustain with your AoE heal, and your cleave to last hit minions, keeping a decent distance between the two of you until you hit 6.
Your first real big damage spike comes from rushing Homeguards on your boots(Usually Mercurial Treads for magic resist and tenacity), followed by Trinity Force if you're building offensive.
