Based on what I am hearing (and my intent to train) I think I am going to use a Shortbow (3s base speed). I would like a composite bow, but I have a feeling that getting the SSI high enough would be frustrating and waste materials.
obsidian, if you are going with a magical short you do NOT need 40ssi to hit 1.25 swing cap.
please click this link, plug in various levels of dex ("sta") and ssi. you will find you can hit the cap with short bow MUCH easier than a comp.
comp you would DEFINTELY want 40ssi on the bow and STILL would not hit the cap! in fact, you need 180 sta and 70 SSI to hit 1.25 cap on a comp. OUCH. talking about some expensive stuff to do that: assassins suit, turqoise rings, or daiymo helm, and very nice armor. still.. within the realm of possibility... *drooling homer simpson style* **** mmmm, assassins suit ****
my lil archer hits swing cap on her magical short with only 155 dex/sta and 20 ssi on her bow. leaving tons of weight available for other mods.
http://uo.stratics.com/content/arms-armor/arms.php
only thing that matters to figure out if a weapon will hit cap is sta and ssi. each bow will hit that 1.25 cap with different amounts of each.
it is very interesting to see how DPS raises at various levels of ssi however. so you may want to play with tac/anat/str/etc. for example taking my archers stats: 140 str, 155 dex, 120 anat, 120 tac, 40 SSI, my archer actually does MORE DPS with a magical short than with a comp. magical short does 34.x dps, comp does 33.x dps. this is because the comp is not swinging at cap! it also interrupts mages better, esp with hit fireball delay. Now, DPS is not the end all be all, for weapon specials matter also. you may want to AI or moving shot in PVP. you might want AI for tough peerless bosses. and thats where the magical would fall short even though it would help you "train better"
one last thing to consider, if you get hit and lose sta your swing speed may drop. so you may want to either consider refresh pots, endurance regen, sta leech, or higher ssi/sta to combat this.
given that you only require 150 dex/sta and 20 ssi to hit cap on a magical short you can eliminate the need to enhance and break items/waste POF/waste relics from your requirement. that is, unless you just like pain or want 40 SSI for bragging rights.

but it would be WAY overkill and a waste of weight on the bow...
i would recommend you just save some crap you find hunting and unravel for the relics. shouldnt cost too much
if you can find a spider slayer tally you can leave that mod off the bow too and put something else like sta leech, hla, or hld
edit: I just realized you claimed that you think you need 35 ssi to hit cap. so either, the chart you are looking at is wrong or you have incredibly low dex/sta. do you have your dex trained to 125? have you eaten a stat power scroll yet? it should be fairly easy and inexpensive to hit 150 dex/sta on any toon: train dex to 125, eat a +15 powerscroll (can be had very cheap, of course +20 or +25 is best if you can afford it), then have +dex and +sta on your suit and rings. presto, 150 sta and only 20ssi needed. lastly, if your str is too low you can always wear mace and shield for str/dex/hld or spirit of totem for str/hci.
a solid understanding of game mechanics (of which I am just a fledgling) will help u create the most efficient weapons for your characters.
my final recommendation:
#1: get yourself to 150 dex/sta and 20 ssi for magical short, or..
#2: get yourself to 150 dex/sta and 40 ssi for comp for ai for peerless (more expensive)
training quicker is a non issue imo, just means a couple extra days before 120.