Welcome and good luck! My advice would be to start as:
49 archery
49 chivalry
22 Bowcraft/Fletching (or whatever amount of skills is available)
In New Haven, do the following (in order specified)
1. Find the tactics instructor. I think his name is Armstrong. Buy tactics to 40.0 by left-clicking on him, selecting Train Tactics from the context menu, and then dragging and dropping 400 gold onto him.
2. Find the anatomy instructor. He's in a building next to the healer. it's west from the warrior trainers, but I can't recall exactly where. Train anatomy to 40.0 from the anatomy trainer in the same fashion as above.
3. Find the NPC that trains lumberjacking. He's near the carpenter in the house North of the moongate but close to the road leading into New haven. Train 20.0 lumberjacking.
4. Go back to the anatomy trainer. Dbl-click him and accept the anatomy to 50 quest.
5. Go to the healing trainer. Dbl-click him and accept the healing to 50 quest.
6. Go to the tactics trainer. Dbl-click him and accept the tactics to 50 quest.
7. Go to the archery trainer. Dbl-click him and accept the archery to 50 quest.
8. Go east out of new haven and find the skeletons, zombies, and spectral spellbinders in old haven. Shoot them full of arrows until you reach 50.0 archery and tactics. Make sure to loot the gold and any relevant items from them.
9. Go back to the archery and tactics trainers, dbl click them to complete the quest.
10. From this point, if you are short of gold, find an NPC wanting to be escorted to the docks. Accept their escort quest and take them to the fishermen on the docks. You'll get 500gp for this. You can use this money to buy an axe or more arrows.
11. If you have enough money, you should consider buying a horse from the stables just east of the docks. It will save you time running around.
From this point forward you can go do some lumberjacking to get logs. You can use fletcher's tools to turn these into shafts. Next, find some birds. I assume they spawn somewhere on New Haven, but I'm not positive. Kill them and skin them for their feathers. You can turn shafts + feathers into arrows using your fletcher's tools. You can continue raising your archery and tactics to approximately 60 on the creatures of Old Haven. Afterwards, you'll probably want to start shooting lizardmen in Despise. There is probably some good "how to" training guide for archery gain at
http://vboards.stratics.com/uo-warrior/213191-warrior-faq-guides-digitally-remastered.html
Please note this was written with the expectation that you wanted to be self-sufficient starting out. You could likely ask in New Haven (or general chat) for some assistance and find someone that will give you a pretty good set of leather armor, some arrows, gold, etc. to start with.