forget about Free options. They have you over a barrel and can change what they want when they want. You can't expect a good service from them either....
There are ways to only buy the Domain name then set up an email forward to your gmail / hotmail address but I would recommend spending the money and buying yourself a Domain name and hosting.
if you want the email address email@example.com
you first need to own the Domain joebloggs.com. This will cost you about $10 (Canadian) a year. Spend $100, buy it for ten years and forget about it.... If you buy your surname maybe your family will split it with you? Remember your family will also be able to get personalized email addresses etc...
Then you need to buy a hosting package. This will basically allow you to constantly manipulate / edit / play with your domain, create email addresses, check them etc etc. You are looking at a monthly charge of around $2-$10 for this service. (depending on who you choose and what services you want).
In short..be prepared to spend $10 a year for domain name, and about $30 a year from hosting. That's less then a dollar a week...so take the jump. Just do your research and find a cheap company and only buy the services you need...don't waste money!