Not really, no. At the point the 2005 series came on, the series had been stopped for almost twenty years. The newer episodes have a nod here and there to the old continuity, but it's not required. I watched the first 2005 episode without any prior knowledge (I had never heard of Doctor Who before) and enjoyed it. you probably know more than I did.
Enjoy! Just give it a bit of time, the first few episodes aren't the best.
Give us a few comments about what you think when you see it, that's always fun.
If you are unsure, I can say this:
The series is essentially about a crazy super-powered alien taking humans on trips through space and time for fun. You have to be able to tolerate a lot of sillyness, but the pay-off is great. The fun episodes are amazing romps, the emotional episodes are deep and tragic, and the best episodes are both. The series as a whole is just grand.
Give it time until Dalek or The Doctor Dances, at least.