T-Mobile Prepaid issue

Hello,

I have a really old T-Mobile prepaid mobile phone that can never find a signal. My mom has a much newer headset than mine and hers has a signal a lot more than mine. If I buy a phone and put my sim card in it, will the minutes transfer? I have 700 minutes on my current phone. Also, would I have to buy a prepaid phone from T-Mobile and just scrap the sim card it comes with? Or, could I buy a phone from Nokia (or other brand) directly without a contract and put my sim card in and it just work?

I'm not too good at cell phone terminology, so please keep it simple. Thanks.