I'd recommend Jax and Blitzcrank as good learning melee champions. They'll get you acquainted with a wide variety of game mechanics (skillshots, next-strike attacks, reactive and passive/active abilities), and have a good mix of killing power and survivability.
I lean almost exclusively towards melee characters in LoL, and they can be a lot of fun once you get used to the pace of the game. That said, the most interesting melee champs can also be the most difficult. Get some practice games with these guys before you try them competitively: Warwick, Sion, Shaco, Katarina, Evelynn, Amumu. Warwick especially is a LOT harder than he appears from looking at his skills.
On DotA experience: one thing you will notice missing in LoL is creep denying. This is a good thing for your melee champion. It means that playing it safe in your lane and just getting exp is a perfectly viable strategy. Your team will thank you for not feeding enemy ranged champions early on.
On staying alive: Armor is kind of a niche stat in LoL. Depending on the enemy team makeup, much of the damage you receive may be magical. Some champions can build for magic or physical damage (Corki and Sion are good examples). Look at their current items by holding down 'tab' to figure out which damage type they are focusing on. When in doubt, health stacking is always a safely overpowered way to go.
Above all, survival depends on not getting caught in unfavorable situations. Always have an avenue of escape and use it before the enemy gank squad gets to you.
On items: In my mind, there are 3 big items that every melee dps champion should consider. 1) Frozen Mallet, or at least a Phage. If you don't need the slow (ie shaco, nasus), don't bother. 2) Phantom Dancer. Look at the stats, you'll see why. 3) The B.F. Sword and it's 3 upgrades. Get to know them, they can all be useful.
Finally, note that lifesteal sounds great for a melee champ. And it is nice, but as a sustainability stat. With a couple notable exceptions (Nasus, Warwick, maybe Mundo), lifesteal will have a relatively minor effect on the outcome of a player encounter. Often simply the lifesteal scepter is all you really want to invest in before endgame, and if you have plenty of HP regen it may be totally unnecessary.