I would recommend starting with "Series 1" of the new version of Doctor Who. I wouldn't try the older episodes to start. Available on demand at Netflix IIRC.
You could potentially start with the series currently airing on cable as it does provide a bit of a new starting point but I think you'd miss a bit and I really think you should start with "Series 1".
Agreed, start with the modern series. Then, if you're hooked, you can explore back into the older versions at your leisure.
Any old concepts that need to be explained again usually are.
"Ohmigod. What are those?"
"Daleks. My oldest enemies . . .," etc.