I think discussing this with your GP (provided s/he is a good listener) is a good first step. Perhaps best to book a double appointment so you've got a bit more time to talk.
I think that you need to think very carefully about what, if any, testing you want done. No test will be able to tell you for definite whether you will or will not get a certain form of cancer, but only your risk; you could be presented, essentially, with varying levels of uncertainty. And therefore, before undergoing any testing, you'd need to establish how you would live with each possible level of uncertainty.
It might also be worth exploring the role of lifestyle and other factors in the cancers suffered in your family. Few cancers are purely genetic, and there may be something you could do to lower your own risk - for example, stopping drinking or avoiding certain foods.
Do you have kids, and if so, do you have any daughters? If so, and particularly if you have daughters, any genetic information you uncover will have an impact on them, and you need to consider how you'd approach that information with them.
You raise the issue of finances. Certainly, it's a legitimite consideration - any genetic information you discover may have an adverse effect on health or life insurance, for example - and worth considering. But unless you're in imminent financial need, it's probably an issue that can wait.
I suppose what I'm trying to say is, please try to calm down and don't allow your panic to propel you into any hasty decisions. But given that you're aware that having a relative your age with terminal cancer means that you do need to consider your risk, you're wise to be thinking it all through now.
Last year, I was faced with the possibility of having an almost-inevitably-terminal, if very rare, disease alongside the possibility of a complicated array of other diseases with genetic components... so a similar situation perhaps not in detail but in urgency and complexity. And whenever I posted about it on MN I got some wonderful support from some very knowledgeable and experienced people. So please, keep this thread going and keep sharing with us your thoughts and feelings.
And apologies for the essay!