New to PC Gaming: Laggy games

[MP2013]

Hi all-

I'm brand new to PC gaming and I just purchased an HP Envy 15 TS. I'm already seeing laggy game performance with some games I bought from Steam. I was hoping you guys could help me out as I'm really excited to finally get back into gaming.

Specs:
Intel i7-4700 (4.7 GHz)
12 GB Ram
1 TB HD - No ssd
Intel HD 4600

I just bought Skyrim and FarCry 3 - most of my issue have come from the latter game. Menu is laggy and cut scenes are extremely laggy. I changed video quality to medium and the cut scenes became bearable but the graphics started acting weird (little boxes of shadow popping up, shading issues, trees disappearing and reappearing..) Gameplay is OK but gets slow every now and then..

My question is - is my PC just not up to standards for gaming? I chose this computer over the Lenovo Idea Pad but I'm starting to regret my choice.. If I should look for another Laptop - what specs are important when comparing to the ones I have? Is RAM causing my issues or my graphics card?

Thanks a million guy.. Happy Thanksgiving!!

-Mike