I am going to build my first own computer, and my question is: are there differences between video cards or can you use them for both amd and intel? Also, should i buy the intel i5 2500k or is an amd processor better in the same price range?
For general purpose computing, Intel has the better processors atm. Bellow $150 amd has some descent alternatives, but higher up intel wins.
Intel does not make separate video cards, you will intel GPUs itigrated in to all thier current cpus, and while they do ok in basic tasks, AMD and Nvidia cards are what you are thinking off. Right know AMD is leading Nvidia with its 7000 series cards, but Nvidia has some alternatives as well.
All video cards work with all modern processors whether it be Amd with an intel cpu, nvidia with an intel cpu, amd with an amd cpu, or nvidia with an amd cpu; it all works together.
Unless you are going to be handling ridiculous work loads, and rendering multi-billion cell spreadsheets, then there is no processor that can even compete with the 2500k in that price range. It is hands down the best CPU for gaming, side by side with the 2600k. So yes, the 2500k would be the ideal option as its unbeatable by any AMD for that price.
Also, you may wish to wait until april 29th when intel releases their Ivy Bridge cpu architecture. It will bring up to 20% better performance than the Sandy Bridge cpu's (which the 2500k is). Right now the 2500k is going for 220$, when the 3570k (the ivy bridge version of 2500k) is released, the 2500k's will go down to about 150$, and the 3570k will be at 220$. In my opinion it is well worth the wait, though that is for you to decide.
AMD and Intel sell CPUs with integrated graphic cores; AMD calls them APUs.
If you are talking about integrated graphic cores, then AMD's Llano APUs have more powerful integrated graphic cores than Intel. However, when compared to graphic cards, even the best integrated graphic cores is less powerful than a desktop Radeon HD 5570. That's not considered a gaming graphic card by any means compared to the Radeon HD 5570 bigger brothers. A Radeon HD 5670 would probably be considered a basic entry level gaming card for desktop PC which should be able to play many games at medium level graphic quality if the resolution is no more than 1680x1050.
AMD's APUs have stronger graphics than the intel integrated, but all pale in comparison to even the lower end deticated GPUs. Would reccomend dropping at least a mid range deticated graphics card in, for example the AMD 6850..etc