Making a Game 101

I would highly recommend finding something you could mod since the amount of work to really create something from scratch or using a 3rd party game engine is pretty high.  From what you've said about experience, this is definitely the best option and will give you design experience while giving you an idea of what it would take to make a standalone game.  I generally don't play platformers, so I don't know of any easily moddable ones off the top of my head.

If you do choose not to mod
Check out Unity and Game Maker.  I do all my work either in Unity or a custom engine of my own, but from what I understand of Game Maker, it will probably be the best choice for someone just starting out without much programming experience.  However, if you plan on making games for a while or want to do work in 3D, I would recommend Unity using C#.  Just keep in mind that it may take a while to get used to how Unity works.

What you will need
The basic rundown of what you need for a game would be player controls, user interface (menus, HUD for health, lives, power-ups, etc), audio (player/enemy sounds, background music, etc.), character sprites (I'm assuming 2D - 3D is more work to make well), background and platform sprites, and enemy AI or movement patterns.  To put it simply, it's a lot of work even for a simple project.  If you want to go this route instead of modding another game, acknowledge early on that it probably won't look good until the end.

Order of development
You will want to focus on the physics and player controls before you do any level design.  If you have to change the physics after doing any level design, you run the risk of ruining all designs you've made already.  Once you have the physics and controls ironed out, I feel like you can do the rest of the work in any order you want, but I personally leave artwork for times when I burn myself out of programming or need some kind of pick-me-up to feel better about development.  I've also heard about working to make level 1 complete to production quality before moving on as it gives you something to show screenshots and video footage of for the rest of production, unlike my approach.  If I wasn't a team of 1, I'd probably lean heavily towards the second approach.

Design tips
For platformers, there's lots of design tips you can find on Google, but to get you started, check out devmag.org's suggestions.