I've been playing about two weeks, and I bought both Champion bundles and have been playing mostly Malphite. I like to think I've been doing pretty well with him, I current have a 14 win 7 loss record, but I can't be a one champion man. :P
I have tons of other champs obviously, having bought both bundles, but the champion that looks most interesting to me right now is Mordekaiser, who unfortunately did not come in either bundle. I have enough IP to buy him, but I'm wondering if anyone has any advice for or against doing so before I do.
What I'm looking for in a champ right now is the ability to rack up a lot of kills, as Malphite doesn't do that so well being a tank, so I want someone more aggressive as an alt character. Is Mordekaiser a good choice for this?

Unfortunately Mord isnt a huge "killer". Thats not to say he cant kill people or anything, but I dont think you will be fulfilled if that is the role you are trying to get out of him. Sadly for you, he often is built as a tank, or partial tank and doesn't have the slows/stuns or damage output to really rack up huge totals.

Mord is an incredible pusher and farmer and in teamfights can absorb a lot of punishment from the other team while dishing out some ok sustained damage of his own. Being a big champion killer isnt what he is known for.

Dont let these comments deter you if you really want to play him and he sounds fun. You will still get kills on him, just not a lot, it all depends how much of a killer you are looking to play. Maybe the best thing to do is wait till he comes free for a week so you can give him a try.

A difficult thing for me to do with Malphite is keeping a significantly higher Kill Count than my Death Count. I know it's not really a big deal so long as we're winning, and I've won a few games with 0 kills and 4 or 5 deaths and a buttload of assists, but it just kind of irks me and sometimes I get distracted too much with my K : D ratio and will blow my ultimate or something just to get a kill when it's not necessary. I want a character to play when I'm in one of those moods.

Alright well can you give any insight to what sort of a playstyle you are looking for, or things you enjoy being able to do in a game?

A good half or 2/3rds of the game can be pretty good at killing. With a few more criteria to look for it might let us pass off some suggestions.

If you're looking for a Champion that racks up kill counts, then Mordekaiser isn't for you. He lacks the crowd control to really chase enemies and finish them off. This isn't to say he won't get first blood or any kills, he just has to work harder than most have to. Mordekaiser's strength is not the fact that he can kill champions, it's the fact that he can recieve punishment and give back quite a bit a punishment thus pushing the enemy back. He's very good at early game champion harassment with his Siphon of Destruction, and mid to late game he can act as a spearhead for charges. His Ultimate, if used in the correct manner, can get you a very early turret kill. His Innate allows him to shrug off most damage and effectively ensures he stays in the game with minimal HP loss.

Most people underestimate Mordekaiser because he's a tank without CC that does minimal damage, ergo they go for the squishy standing behind him. You can make people pay seriously for doing this.

Overall, Mordekaiser fulfills the role of a tank very nicely. His usefulness, IMO, stays consistent throughout the entire game. A late game Mordekaiser can essentially make or break a game. However, if you're looking to rack up kills, then you're better off with Master Yi, Twitch or maybe Garen.

Given that this was a topic pertaining to Mordekaiser, I stuck mostly to Mordekaiser description, hopefully it gave you a little insight into what Champion you're going to choose.