Antarian troops are not good for sieges overall....Marinian, Rhodok, and Villianese are best IMO. The only time I see heavy losses is when I'm assisting an ally on a siege, defending an ally's holdings, or forced to order my archers to charge the walls instead of just holding position and sweeping them clean...and in the first 2 scenarios, the heavy losses are NOT mine.
Basically, when I start the siege, I immediately order Hold Fire (long range = less accurate, waste of ammo). Order to Hold Position at a good wall ranging distance, which all or most of my ranged units will have no problem reaching since they pull out their shields when ordered to hold fire, then order them all to stand closer 2 or 3 times so half my force isn't sitting way off to one side or the other never shooting a shot, and then finally order them to fire at will.
Once the initial pack of enemy are swept off the wall, I order hold fire again so everyone isn't shooting at the same leftover unit or three (again, to prevent waste of ammo having 30 arrows strike the same target), wait for the next wave to cluster around the wall breach site, and open fire again.
Using those tactics with nothing but ranged units in my siege warband, I'll clear 150-200 units out of the pool of defenders before running out of arrows/bolts, at which point I order the charge for cleanup.
Cleanup phase gets expensive, especially if there are a significant # of enemy heavy infantry/cavalry still alive...but as soon as my first reinforcements wave appears and charges into the fray they'll do as much shooting as meleeing...and the remaining enemy will fall like wheat to a scythe.
As for how I start out: If I'm not going to 'cheat' by importing my incredibly rich current character (36 million in the bank generating 600k+ per week interest, another few mil built up in the treasury, and a few mil on hand for training and such) then I just take my initial troops and haul them around from melee tournament to melee tournament. I say melee because tournaments that feature primarily ranged fights are almost guaranteed losers early on until you get your health and archery/crossbow skill way up. Save before joining the tourny, and then bet max every round.
Good tournaments to join are anything except Rhodok, Marinian, or Villianese..all 3 factions feature more ranged than melee. Nord and Zerrikanian tournaments are VERY easy to win since there's almost no ranged...it's all axe/shield or heavy swords.
I prefer to use a bow instead of a crossbow because you can shoot faster, and once you get your strength up for higher power draw levels, and your bow skill up for accuracy, you can still 1 hit pretty much anything. With a bow that requires PD 9, using 1 large quiver of +9 arrows and 1 large quiver of +12 (haven't found another +12 batch anywhere yet), my average damage per shot is 90-100.
While doing the tournament circuit to build up levels and money keep a close eye on the political scene. In the event that things are shaking out into alliances that are strongly lopsided (4 vs 8 for example), you might consider joining one of the 8 temporarily just to sow dissension by attacking caravans belonging to one of that faction's current allies...and then abandoning the faction. If there's a faction who hasn't formed alliances yet, you can start scouting all their castles/towns for one with a small garrison that you can use to start your own faction.