Once you find a type of game you like or feel comfortable with (be it a platformer like Mario or a first-person shooter like every other game in stores), start to try out other games in that genre. I find a lot of customers that come into my store are generally put off by certain genres or types of games rather than specific titles themselves. You’re more than likely to find loads on top of loads of awesome experiences within your genre. Once you’ve plundered those, try a new genre and branch on out. You may be surprised to see what you like. The Xbox 360 has a storied catalouge of demos for you to download and try off of the Marketplace so don’t feel like you have to take a gamble in a video game shop when you can demo a game for free.
As for Skyrim, it is the fifth game in The Elder Scrolls series but don’t feel pushed to play the last four; like most role-playing games of its ilk, Skyrim can thoroughly be enjoyed as a standalone experience. It’s a massively open-world fantasy game where you can explore, interact, and take on quests at your own pace. There’s seriously hours and hours of playtime to be had, and the customization options for your characters, equipment, and in-game choices are diverse enough to make the game habit-forming.
If slaying dragons, absorbing their souls, and shouting a thunderclap into the sky sounds lame to you, then avoid Skyrim.