Intel are often seen as given better performance, whereas AMD are seen as being better bang for the buck. Tbh you can get either and you won't notice any difference but I'd usually recommend Intel. Then again, if you're trying to keep costs down it's always worth considering AMD
As for cores, more cores means more processing power, in its simplest terms. It really depends on the program; if a program can only use 1 core, then a single core processor would be best, but if a program can use 4 cores, a single core processor could still run it, but just not as well as a quad core processor. However, if you look closely you'll see that (9 times out of 10) the more cores a processor has then the slower each individual core is.
For example say you have 2 CPUs; CPU 1 is a dual core running at 3.5 GHz, CPU 2 is a quad core running at 3.2 GHz.
If a program uses two cores at max, then CPU 1 would use both cores with a total speed 7 GHz, CPU 2 would use 2 cores as well (leaving the other 2 idle) with a total speed of 6.4 GHz.
If however, a program could use up to 4 cores then CPU 1 would only be able to use 2 cores at a combined speed of 7 GHz. CPU 2 on the other hand would use all 4 cores with a combined speed of 12.8 GHz, a lot better than CPU 1.
You may now be thinking that there's no point in getting a dual core processor (besides the price) but putting theory into action, the majority of modern games only use 2 cores, with very few just managing to utilise 4 cores.
Quick summary - AMD or Intel, doesn't really matter, just comes down to brand preference most of the time. Quad core is faster than dual core but only in certain situations. For you dual core will be fine, but if you have spare cash it may be worth upgrading to a quad core, but it's up to you.
And just in case you're wondering, no it's not worth getting a hexa/octa core processor. Yes they would run faster in certain situations, but those situations are few and far between.
Just on a side note (after just noticing) your mobo is a micro atx. Were you aware of that and do you know what it means?
P.S. Sorry if my explanation was a bit too much or too technical but somehow that's the easiest way for me to explain it.
Edit - And to think this was a 'quick reply'