IPhone 4s to 5 and computer

I have a problem because I have no experience in technology. I got an iPhone 4s about a year ago, and I have iCloud and an Apple ID. Lately I have been getting all these reminders that icloud can't back up due to my lack of storage. I looked at my usage and noticed my camera roll is huge. I need to get these pictures off my phone somehow. I asked my friend and he said I need to buy a computer and download them into it. Also when I get an iphone 5 ( which I'm in a few months) I need to use icloud to get all my stuff I have in this 4s to the 5. I don't know how to do that though. I just changed my icloud password because I had forgot it. But I also don't have a computer. My question is how do I get all my stuff from the 4s to the 5? Do I just type in my icloud password and it will download all my stuff? Or do I have to hook it up to a lap top? I also need a lap top to clear storage. Do you have any recommendations? Do I need to get an apple so it has icloud or could I use any computer? All of the transfer stuff I need help with ie. Music, pictures, videos, social media, etc. Also, would the 4s' stuff be different on the 5? Any info helps.

All your stuff will not be stored on iCloud, only some of it. If you go to an apple store they may take care of it for you. You can use a PC or an apple to download your photos. It's pretty simple, all you do is connect the iphone via the USB device. Then, the iPhone shows up as a drive on your computer. Open up the drive and you can copy all of those files directly to your computer.