In Latvia, there is produced a lot of spirits, so I can't really mention all of them.
The best and safest choice of them is available in the Stockmann centre (near the Central Station). You may look up there.
In the recent times,
Riga Black Balsam was the #1 traditional Latvian spirit drink, but I don't like it now. Probably they changed the recipe in production.
The best vodka I remember from the winter times, was "pepper" vodka. I don't remember the producer, unfortunately. It is sold in squared glass bottles and has kind of "golden" letters on the front. It's called something like it's "Ukrainian Pepper Vodka", but on the back cover, you will see it's produced on Maskavas street in Riga

But that's really a good vodka. Not sure if it's still on sale!
I think, there wouldn't be major problems to get couple of bottles via plane, but only if you have a "full" luggage with you, i.e. you don't take bottles to airplane, as it's forbidden by EU regulations.