There is a whole world of tests to do. First, the doc should do a background on you so it would be good to have a timeline set up prior to give him as much info as possible. Second, the doc should do a thorough neuro exam, reflexes, look for weakness, etc. Third, will be a whole lot of blood tests to rule out other problems. Fourth, a MRI with MS protocol and w/wo contrast should be ordered, this is the big test. He should do a spinal MRI also. All that will paint a pretty good picture.
From there a Lumbar Puncture might be ordered. I think it is a good test to take but since it doesn't mean a lot if it's negative and you don't need it to get diagnosed some feel it's unecessary. But, if it is positive I think it's a really good indicator.
Other tests can be the Evoked Potential tests but I would think that is further down the line after the rest of that. Unless they suspect Optic Neuritis.
I would think that a good neuro would be perfectly willing to go into this stuff with you considering that you have family history, are from the northeast, etc. There is a possible genetic component that would raise your chances but as far as I remember it doesn't make the likelihood that you will also have MS shoot through the roof.
I'm no doctor, this is a really watered down version. I'm sure other people will chime in and give you something more informative or make corrections to what I said. Every person and every neuro is different. This is just kinda how it went down with me and your average path if the doctor does feel it's possible MS. Meds are important to start early but it is also very important in my mind to get that MRI done. If your stuff isn't clear cut, which it almost never is, it is very important to have that baseline MRI for comparison purposes. This is what the MRI looks like now and this is what it looked like a year ago.
So, medical history and symptom timeline, neurological exam, blood tests for mimics, and MRI is what you should be looking for in the start of this. From there it all depends on what they think is going on, if they think it might be MS, etc.