A premade module is always easy, it's not my choice. I'll tell you how I and other people I play with do things, but it probably won't help you out too much.
The first thing is to decide whether to use a premade world or a custom. I honestly wouldn't say which is easier. If you go for a premade world, it sounds easy, but the DM has to read all about the world and really hammer it out. He has to drop some things and add others, and be careful not to introduce contradictory ideas. If the DM creates the world, it's all his and he can be confident that no contradictions will exist.
Since you're new, I suggest using a premade world.
The DM will have to pick a place to start in the world. This will involve a lot of time. It's not easy to be a DM. But then again, there are lazy DMs. If you've got a guy you all like and can run a game well, you're lucky. That's the most important thing.
Ok, so now you've got a place. You need a game. This is where a DM should create something all on his own. But he will need some inspiration. The first place is the DMG and the 100 adventure ideas listed there (it's in 3.5, I assume something similar is in 4th). Also browse 1st edition modules. They can readily be adapted to whatever edition you're playing. The catch is that you have to completely remake the module. It's for inspiration, not direct use. When there are fantasy books I've read and I know my players haven't, I steal ideas from those. The characters hopefully have backgrounds, so you can always take something from there.
As I said, not much use. The question you asked is what to play next, and my answer is that it's up to your DM to come up with something. Sure, you can always buy modules. In my mind, playing a module is only slightly better than playing a video game. But then again, I also wish I had more spare time because designing dungeons, creating NPCs, and coming up with quests take a lot of time.
If you want to read about my campaign, it's
here. Start with Part 1, of course. It might be hard to follow since my log is intended for the players to keep track of what has happened, not for other people to know exactly what transpired.
That's my style of running a game. Everyone does it differently, of course.