I think I'd take the train too - the bus option is cheaper, but about double the journey time of the train, and a little more complex.
As I am travelling the 22nd of Dec, am I able to purchase a ticket prior to travelling over to Japan as per the website so as to reserve a seat? Or do I need to purchase one at a counter at the airport? Just wishing to make sure that I can actually gain a seat that night as I am sure the trains become very busy.
Although it is possible to reserve a seat in advance at the JR-East shinkansen reservation page selecting the option for 'No JRP traveller', to use this service you must collect your reserved seat ticket at least by 9pm on the day before travel or it will be cancelled. I think this means the service is not suitable for you as you will arrive to Japan on your day of travel.
Although you won't be able to reserve a seat using the online service, I don't think you will have much trouble getting a seat on the day. The main December festival in Japan is New Years Eve/Day. Christmas is a relatively recent import, and doesn't imply the same family get together that it does outside Japan. That said, if your flight is a very late arrival, I recommend you call the english speaking JR-East infoline to see if they can help you further.
Also, as I will be travelling with some luggage, just your standard 1 metre high box type of luggage, is there a compartment to store my luggage or will i need to keep this by my side. Would this then be a nuisance to other passengers?
Large luggage can be left in an area behind the last seat in each carriage in the direction of travel and is totally acceptable. If the luggage is small enough there is also an overhead shelf running along each side of the carriage.
Also is a reserved seat best or an unreserved seat best for a long journey (i.e. Tokyo to Sendai).
I like travelling with a reserved seat if I'm travelling with friends as it guarantees that we sit together, especially at rush hour times. However if I'm travelling alone on a standard ticket I often ask how busy the train is at the JR ticket counter and base my decision off that. I've noticed that often the unreserved seating cars have less people than reserved cars, so they can often be a good slightly cheaper choice if the train is not busy.
Hope this helps!