We strongly advice to come by air, in this case you don't need Belarusian visa (more details), and firearms and trophies procedures are very quick. Coming by own vehicle will keep you for hours on Polish or Lithuanian border both entering and leaving, and you will have to pay the roads in Belarus (which is not too expensive but a bit painful).
The list of European cities connected with Minsk (MSQ) by direct flights. If you buy the ticket with Belavia don't forget to call and warn them thet you carry guns, they charge 50 € for each way for the kit one arm + 5 kg of ammo. If on your way back home you have a trophy of moose or red deer (we will pack as required by air company) they will charge you the usual 50 €.
Actually there are no flights from Europe to Belarus, to get here by plane you should come through Istanbul.