Where should a girl start online gaming?

I have a laptop with windows 8 (terrible i know.) and i want to start with Steam and things? I like minecraft and pokemon but i want to do something new. I don't want people to think i'm doing it to look cool and go straight to like COD or something. Can someone with a good gaming experience tell me where to start and not look like i'm trying to hard to be a "gamer girl"? Because i just wanna know what's fun and easy to start with?

The most popular game for all genders out there right now is League of Legends.

I won't say stuff like "Because your a girl… Etc" but I advice you to start with:
The Elder Scrolls V: Skyrim
XCOM: Enemy Unknown
Bioshock 1 (If you like it, then in my opinion you can try anything else) Also try after it Bioshock 2 and Bioshock Infinite
But if you find Bioshock 1 hard then just go for Bioshock infinite (Although i don't recommend that).
Hitman: Blood money.

You like strategy? Go play Age of Empires or Total War Series
You like MMORPG? Go play Eve Online
You like FPS? Go play Battlefield
You like Sandbox (Besides minecraft)? Go play Garry's Mod
You like Free Roam? Play the Grand Theft Auto Series ( I recommend San Andreas.
You like Indie? Go play DayZ ( Pew Pew on Zambies! )

But if you really want to go dangerous I recommed BIT.TRIP Runner.

Hope this helps.

Not sure what genre your interested in but here a some things you should have in your Steam library and are relatively cheap and can run on a laptop.

Half Life series,
Portal,
Counter Strike Global Offensive,
HitMan series,
Garry's Mod,
Space Engineers,
Dragon Age and Mass Effect Series (prob best to get these on Origin)

Edit:
I forgot about Civilization V, well that is if you enjoy turn based strategy gaming.

You should try Dayz, it is a little buggy because it's in alpha but it is an amazing online game.

Portal, LoL, WoW, Counter Strike, Garry's Mod, Skyrim, etc.