what happens when the period of registration ends?
I am going to get a domain name and start a web site. I wonder what happens after a year or two when the period of domain registration ends. will they be able to ask unreasonable price to expand the registration?
is there any difference who we register our domain through?
It depends on who you pick for your registrar.
Most charge the same price for new domains and renewals.
If they try the bait&switch and raise the price on you then you can always just transfer it to a different registrar.
I do mine through AIT - aitdomains.com
I like to register my sites through luckyregister.com which is basically GoDaddy but a few bucks cheaper. Also, you can click on autonrenew so you don't have to remember when you need to plunk down another 8 bucks.