(making a person "jump" in a game is NOT FUN Omg.)
LMFAOOO!!!! You just took me back to my good ol' days...I bet I still have about 10 different 'demos' where I attempted to get 'jumping' in. Yeah, i do remember that being a real bitch. xD
As for what project to do...That's fully up to you. You never have to 'scrap' a project--you can always come back to it later when you're more experienced. I'm not sure how much you know about C++, so I really couldn't reccomend anything to you.
However I will say this: if you don't think you're ready, then seriously, don't try to start out using a graphics API. You can learn the language just fine from the DOS console, and create games there just as well.
Or, if you insist...Don't start out with a whole, complex 'game' in mind. Perhaps try making multiple applications with single goals in mind? "This app will demonstrate jumping" "this app will demonstrate collison" "this one is joystick tests". Then, after you've made a few, you'll feel confident that you can put it all together into a larger unit: a game.
Hope I helped. All I could really think to say w/ given info. Lol
Oh, yeah..And for the side scroller thing...Gyro and JS Lemming made a side scrolling shooter Demo a while back in SDL that I think i still have the source to. It was a learner's thing, and was HEAVILY commented. It's in NO shape to be made into a game as it's written (lotsa globals, no real central structuring, not really object oriented) but the concepts are there. If you'd like to continue your project and have a look at that, i doubt they'll mind. It's a great example of making a 'level' through arrays, jumping, movement, shooting, graphics, sound, etc.