Correct. Right now, both servers are located in the US, so you won't notice any significant ping/lag/latency difference. However - as you said - the EU server will be moved to Europe (I think Frankfurt, but don't quote me on that).
That being said, it's hard to say how/if latency will change for you. If you don't have any issues so far, I wouldn't worry too much about lag alone. It can't get worse, it may only improve.
Geographically, I'd assume the European server would be the better choice for you, since it's quite a bit closer to you. This also means that your prime time won't be that far off compared to other players playing there.
Overall, you should try to see where your friends are playing, assuming you already know people you'd like to stick with for this game.
What you definitely should keep in mind are server downtimes, which will follow different schedule for NA/EU as stated here (you might have to try to open that link twice for it to show the proper article for whatever reason):
Tuesday (Patches)
00:01 am EDT (06:01 CEST) - EU
08:00 am EDT (14:00 CEST) - NA
Friday (Reboot/Hotfixes)
00:01 am EDT (06:01 CEST) - EU
08:00 am EDT (14:00 CEST) - NA
North American Megaserver
Tuesdays at 8:00 am EDT (14:00 CEST)
Fridays at 8:00 am EDT (14:00 CEST)
European Megaserver
Tuesdays at 00:01 am EDT (6:00 am CEST)
Fridays at 00:01 am EDT (6:00 am CEST)
After all, you most likely don't want downtimes to happen during your playing time all the time.
Best Answer
Yes, you have to buy it on every platform you want to play.