Offhand, I'd say that the stuff listed in the books are essentially stock. Some droids like the assassin droid, or battle droid will have variable skills and equipment (with the listed stuff being typical or suggested) but the more common droid types should "start" as listed, with the players rolling adding or taking away from that.
As for making and customizing your own... it's up to the GM. You're basically asking if you can exchange credits for either a party NPC or a second PC for you. How that exactly works will ultimately influence his decision.
If you are making a secondary PC for you, then it should probably follow standard character generation, just for simplicity.
On the other hand, if you just want a party NPC to run around with, then it really is just up to the GM to generate a baseline that fits the mold you're looking for, then adjust it based on your Negotiation or Streetwise results when purchasing. Advantage = R2-D2, Threat = Chopper.
If you want to upgrade your new purchase, again ask your GM.
If I were your GM I'd probably set up some kind of basic template, then work off that.
Example (that I am pulling completely outta my butt right now):
Player wants a covert security droid to protect his combat-inept character. The player doesn't want an outright secondary character to manage completely, just an NPC he can roll in combat for while his primary PC hides under the table and pees himself. Outside of combat it's a normal NPC, not intended to earn XP, advance, ect., and typically not directly controlled by the Player.
Purchase starting droid: Player goes with Protocol Droid (so just use the book for initial acquisition)
Once he's got the droid, he'll need to install skillware, hardware, and weapons.
Depending on what the player wanted to do, I'd have him roll to "search for parts and software" especially if the stuff he's looking for it really out there. Improving your droids Kno:Education skill is no biggy... but Improving his Ranged:Heavy isn't the sort of thing you can just buy in the automation section of your local TaggeMart...
Equipment can be purchased and installed normally.
So he buys a holdout blaster for it's hide bonus, and adds a filed front sight to grant the droid quick-draw. (Narratively he says it's in a hidden compartment, that flips around and replaces the droid right hand in combat.)
Armored clothing is just redressed as "low profile armored plating." but statistically no different.
Skillware: The player can either just add the skills and hope for the best, or attempt to revamp the droid to be more of a combat model.
Basic Skills: I'd say the skills a droid comes with are it's analog to "career skills" and the others are not. To upgrade those skills, I'd say it starts at average Computers, and increases difficulty by one for each rank. Noncareer skills can be improved the same way but difficulties are always upgraded at least once. Cost is 100x the intended rank improvement level for "career" skills, and x200 for "noncareer." Failure means you've "ceilinged" the skillware and the droid cannot improve it's skills anymore.
Skillware refit: If the starting unofficial career skills of the droid doesn't match want you want, it's 3,000 credits and an upgraded hard check. This allows (with GM's consent) the player to add a new career skill to the droids list. Sufficient advantage triumph can allow additional skills or allow a skill to start with a rank.
Talents: I'd go with Minions can take none, Rivals up to 3ish, Nemesis 3ish or more. For a droid, a Talent represents not just upgrades to it's software, but may also require upgrades to it's physical hardware as well. Installing a talent requires GM consent, and costs a minimum of 500 credits (with "better talents" going up in price rapidly), is at least a hard mechanics or computers check (depending on the talent in question) and should be upgraded once for every existing talent the droid has. (so our pal adds the talent bodyguard, which the GM says costs 1000 credits, and is a hard check, since the droid has no stock talents, though the GM might also decide to upgrade it since the talent is pretty far outside the droids original purpose). Like with skillware, failure means you've hit the droids limits and you can't attempted to install further talents packages.
Base Abilities/thresholds/ect: Can be adjusted by installing the appropriate talent. It'll be expensive, and rather limited, but droids are built to pretty specific specs, and exceeding those isn't easy.
It's not perfect, and I'm sure someone will poke plenty of holes in it, but at it's core it allows you to affordably and safely improve a droid within it's intended role, but the more you do, and further outside the intended design of the droid you go, the more likely it is you'll blow a pile of credits and just fry the poor bot in the process.