Wait, a maximum of 3 magic items at level 15, and no more than 20k each? Your DM does realize that 15th-level PCs are expected to have, on average, 200,000 gp worth of equipment each, right? Does he plan on making up the difference with treasure in-game? If not, you guys will be woefully under-equipped, and the non-casters esp. will be at a severe disadvantage when it comes to keeping up? That rule makes the Cleric and Druid ridiculously better than everyone else (hope they invest in Chain Spell).
Given that, if you craft the item yourself, can it be up to 20,000 gp at the crafted price, or is the cap on the market price? If it's the former, be a spellcaster and take Craft Wondrous Item. Possibly take Craft Magic Arms and Armor as well, depending on how you want to go. Make all your gear, and use whatever cost reductions you can to get more value out of it (10% reduction to restrict it by class, 10% reduction to require a specific skill, 10% reduction to restrict it by alignment, the stacking magic items reductions, etc).
I really can't advise playing a non-caster with those item rules. It's a simple fact of the game: you need the bonuses from magic items to compete as a martial-type, esp. at high levels. Not to mention the array of resistances and immunities that are necessary to survive combat in a high-level environment, which will be hard if not impossible to come by under those rules.
Yes, the DM is perfectly aware that our characters are far below our expected WBL. That was the idea. Ever heard of a low-treasure campaign? Maybe the DM's planning to rain loot on us once the game begins, or maybe not, I don't know. Some other players have mentioned crafting, though I don't know if they're going to make something above 20k market price (so far the discussion is just some players trying to explain the crafting rules to someone who isn't too familiar with 3.5). I know it's not wise to play a non-caster at this level. That's why I'm planning to switch to Unseen Seer.
Anyway, I'm considering the build Factotum 3/Wizard 5 (Spontaneous Divination)/Unseen Seer 7 right now. Thoughts on spell selection? I'm thinking Hunter's Eye and Divine Insight as my advanced learning spells, but I'm not sure what to pick the next time I get it. Please keep in mind that I'm trying to maintain the flavor of an Assassin -- subtlety is a plus.
I think Echoes is just worried, and, in my opinion, rightly so, about whether or not your DM is aware of just how badly being denied your character WBL affects the CR system suggested in the DMG. While it's certainly not an exact science, being denied appropriate wealth in magical or mundane gear can cause your characters to function as much as three levels less than they actually are, if not more. Has your DM ever run a low-wealth campaign before? Is it specifically low-wealth, or is it more low-magic? Is it a combination of both? If it is low-magic, are there as-of-yet-unmentioned penalties to casters? It's one thing if he just doesn't want you to go ape-shit with equipment right off the bat, and wants a little more control over the first few combats of the game, but knowing for sure which way this is going now so you can plan around it is more important.
Not making these kinds of campaigns an exercise in frustration for the players is really, really hard.
Anyway, the fluff and flavor of being an "assassin" is all in your mind. Arguably the only really effective way to be an assassin is to be able to kill someone, no matter who they are and do it without getting caught so you can survive to do it again. The actual execution of this is largely irrelevant. Someone who walks around everywhere in black clothing with a permanent scowl, a scarf wrapped around his face, and several vials of poison in his belt pouch is probably the worst assassin ever (*cough* Altair...).
In feudal japan, the most common disguise for ninja was as a farmer or peasant. Some of the (supposed) best assassins in history were women. Anything you can to disarm your target, mentally and physically, including acting like a clingy, lonely, drunk in a bar that he or she might take pity on, will make you more effective. That has everything to do with your personality, alignment, and role-playing, and almost nothing to do with your class selection and character build, aside from possibly skill checks.
That aside, I'd suggest the Abrupt Jaunt conjurer variant from PHBII for your wizard levels. You give up your familiar, which you probably won't use much anyway, and gain the ability to teleport 10 feet as an immediate action (like after an enemy hits you with an attack roll, but before they roll damage). This will keep you living.
If the DM is keen on having you hunt NPC's down, Bloodhound (SpC) is also a possibility, allowing you to immediately reroll a failed Survival check to track someone for the duration, which is a full day. At higher levels, Implacable Pursuer serves the same function. Soon as you see them once, you will always find them for the next hour/level provided they keep failing Will saves. It will even tell you what plane they went to. If you fancy having the DM handing you his notes every combat, Know Opponent and Know Vulnerabilities are good candidates as well, as is Omen of Peril if you'd like to get the gist of his notes for everything else.
Depending on how lenient your DM is as to what he considers "physical contact", a metamagic extended Chain of Eyes (SpC 45) can either be useless or one of the best spying spells ever. Consider this: you forge an extremely official looking letter to a king and personally drop it off to a courier. Once he takes the letter from your hand, you cast the spell on him. Once he passes the letter to the next person, you transfer the spell to them, and so on all the way up the chain until you reach one of the king's personal servants (or the king himself). For extra added fun, find an excuse to drop a Listening Coin (pg 133) in the envelop as well.
For more emphasis on the killing, Find the Gap (SpC) allows you to resolved the first attack you make each round as a touch attack. Nabbing Grave Strike (SpC 107) from the cleric list so you can sneak attack undead (unless you already have a way of doing so) is also a candidate for unseen seer advanced learning. Same goes for Vine Strike to sneak attack plants. Sniper's Shot will allow you to sneak attack a target regardless of the distance between you which can make for some truly epic long range assassinations.