Hello there, I'm pretty new in the audiophille stuff (new to the forums too) and I want to venture into this new hobby.
Howdy and welcome.
First of all, my Grado SR60i will be arriving soon because I wanted to try a good headphone because I'm tired listening music using 10$ headphones. So here's my question.
Good choice on headphones.
Are laptops are a good source to play music? Will using a better headphone change/show difference the quality of the music or it will stay the same? Do I need to buy a better audio system to unleash the potential of my SR60i?
Highly variable. Computer audio can be very good, but it can also be very bad. Basically I'd suggest worrying about the following things:
1) Quality of encoded/ripped media. Basically you want stuff that was ripped right, and that isn't overly compressed. Generally that's 320k mp3/WMA or better, but depending on the content, 192k can still be perfectly suitable.
2) Quality of the computer's output equipment. Basically you want a "clean" output to your headphones (or the amp driving your headphones) - if there's buzz/hum/noise coming from the computer, that you can hear, it has the tendency to get annoying after a while.
Regarding if you'll notice the difference with the SR-60 and nothing else, I would say yes - you absolutely should! Grado headphones tend to be very easily driven as well, so assuming your computer's output is clean, it will probably drive them. The biggest/most important factor in an audio system is the output device (headphones, speakers, etc) - so that's a good place to start. Everything else between the music and that device is basically there to make sure the headphone/speaker is driven properly, and that the music is handled properly.
And FLAC, are they worth it to download than the MP3s? I have some CD albums too but there's also some mp3s I downloaded for those music I can't purchase from stores. This will lead me to redownload all of them in FLAC, so will it worth the hassle?
It really depends. If you've got good 256k or 320k rips, you probably wouldn't notice much of a difference getting FLAC (or other lossless) files. In the future, I'd suggest lossless when available - just for piece of mind more than anything else (and having a lossless copy of the data is always "best" - you can always compress it down for mobile devices or similar at a later point, but you can never un-compress a lossy file).
If you've got CDs, you might re-rip a few to see if it's a big deal for you.
If you're starting with a bunch of horrible 64-128k mp3s though, you may want to re-think that. Of course if there's no other way to get the music, there's no other way to get the music, but by and large less compression is a good thing.
And thirdly, DACs. Can someone explain to me simply what are they and are they worth it for audio quality?
Long answer or short answer?
Short answer is DAC stands for Digital to Analog Converter, and generally in audio circles it means a standalone device that performs that function. Your computer will actually have a DAC in it already (so will your cellphone, your mp3 player, etc) in order to produce an audio output, but a lot of folks want a more premium solution. In some cases I will say it makes sense to buy, in others not so much. Basically if you already have a clean output, I wouldn't dump a ton of money into it.
You may also see the phrase "USB DAC" appear - which is somewhat of a misnomer. So-called USB DACs are what was known a few years ago as "USB Soundcards" - basically it's an audio interface (some have headphone amps built in, some have audio inputs, some are just stereo audio outputs, etc) that connects via USB, as opposed to some other interface (like PCI). They're popular because they can be hooked up to laptops or desktops, and in recent years a lot of marketing has been put out as to why everyone "needs" one. If your computer's built-in audio hardware is kind of dumpy, a USB solution wouldn't be a bad choice, but I'd honestly steer you away from spending thousands (or millions :rolleyes

of dollars on DtoA converters or other fancy electronics like that - clean is clean.
Maybe this article will explain a bit more:
http://en.goldenears.net/index.php?mid=KB_Columns&document_srl=1921
Extra: I read some reviews about them getting huge praise and I managed to grab SR60i at 50$, anyone want to share any experience with them?
I'd agree that the SR-60 are a fantastic headphone. I think that by and large they're a good choice as a first headphone, and unless you're expecting a bass-blaster, they'll probably put a smile on your face. That said, you'll likely find relatively mixed opinions of Grado headphones, as they tend to be some polarizing (primarily along the lines of looks, fit, and their relatively unique sound signature).