Floor pump, frame pump (Blackburn), sticky patch patch kit, multi-tool or only the Allen wrenches you need (get chain tool later if not right away, but do get it), spare tube(s), under-the-seat bag to carry stuff in, clipless pedals, shoes, shorts, t-shirt or jersey (jersey pockets can substitute for under-the-seat bag some of the time or in the beginning), helmet, headband, computer, water bottle cages, water bottles, and that's the whole thang. Shop at Performance (they have a sale going right now, including winter clothing), join Team Performance which knocks about 10% off (you get 10% in points toward the next purchase, but the prices are a little higher than Supergo or Nashbar, all owned by the same guy (?)), and you get free upgrade to two-day shipping, so there's no wait.
I prefer to start new people in clipless pedals. If they are small women I may run the release tension down so they can't possibly get stuck. When people want to dab the ground they always want to go sideways and down to get to the ground, and that always gets them out of the pedals. Try that with toe clips and straps and you won't go anywhere. There's no additional risk compared with platform pedals. Just try leaning against a wall and getting in and out about ten times and you should be fine. Anyway, you've got to learn to pedal all the way around the pedal circle, and you won't do that on platforms. If you don't switch to clipless pretty soon, you will be handicapping yourself next Spring because you won't know how to pedal.
I would try to get most stuff besides the bike someplace besides the LBS, unless I was going to be doing the shop rides soon. They will take you to the cleaners on accessories. Just give them a little bite.
If you are in a warm climate and are of moderate or larger size, when you order water bottles, get the Zefal Magnum water bottles, which are reported to hold between 29 and 33 ounces (depends on who you ask). If you think that is too much water, just consider the extra weight as a training aid on hills. Staying hydrated is a significant performance enhancer (thin blood pumps easier and keeping your body temperature down with more perspiration helps too), and sometime next summer you will be glad you were carrying more water than your partners when they have to skimp to make it to the next stop and you don't.
I'm not super-comfortable with recommending a particular pedal format. There are a lot right now. I think you can't go wrong with the $30 Taiwan SPD pedals, probably sold by both Performance and Nashbar right now. You can put those on a mountain bike later, or even throw them away. I'd leave them on the top shelf in the garage as spares. This supposes the bike does not come with pedals on it.
As for shoes, I like ones that fit and have a ski-buckle closure back by the ankle. That closure is repairable and lasts forever and holds an adjustment. I'd rather get laces than velcro.
The road shoes usually have stiffer soles than MTB shoes, so if I thought I was going to be a dedicated pack-rider roadie, I'd get road shoes. If I thought I was going to be a tourist or an MTBer, I'd get MTB shoes.
I was a bad (as in not very good) bike racer back in the early '80's, and I had endless trouble with toe clips and straps. If I had known about those Cinellis M77 pedals (first modern clipless pedals) I would have bought them. My problems were:
1. Breaking rear plate on quill (what the heck is a quill on a pedal anyway, and why do they call it that?) pedals where cleat slot fit. They'd split right down the middle. 180-pounders with watts do not do well on Euro-parts.....
2. Toe clips do not come in sizes that are large enough. The requirement is that they clear the front of the shoe with the ball of the foot over the pedal spindle, and still have the slot where the toe strap goes through far enough back to keep the strap behind the knuckles on the little and big toes. On the knuckles or in front of them is bad. Lots of people don't know how they are supposed to fit, so the shoppies would offer to shim them forward so they would fit, but when you do that you also move the slot forward, which ruins the strap fit. Dumb.....I was getting ready to build my own toe clips large enough for my size 48 cycling shoes when I found some KKT XXLs that just barely fit.
3. No leather or synthetic strap available back then, including the Alfredo Binda Extra laminated straps, would last more than three weeks with pulling up on hard hill climbing. I'd just rip the teeth through the leather until they had cut matching grooves, and then they wouldn't hold any more. I did buy a set of the Performance plastic ratchet straps right at the end of the toe strap era, and I think they would have lasted a long time, but I had already moved into Looks. Before that I had ended up doing just what the trackies do, using TWO straps per side, looping the second strap through the back plate and around the shoe and back. Strap problem solved, but I was still breaking pedals......took longer to get out, too.
The second day Look pedals were available in Dallas-Fort Worth, I bought them. By then I wasn't discovering I was going to be a bad racer any more, but I knew that since they didn't have the back plate that kept failing on the toe-clip-and-strap pedals, they wouldn't break like that.
I hate toe clips. The durn things were torture devices, with hard metal always going after my foot and straps crushing my knuckles if the toe clips were too small.
I used Looks for a long time, but I eventually decided the plastic cleat was a safety hazard unless you replaced them early in the wear cycle. After you have broken the tab on the front of the cleat once or twice with full-power uphill standing sprints with lots of pulling up, you won't want to do that again. I'm not as strong as I was when I was younger, but I trust the metal SPD cleat and the cleat and pedal design to keep me in when I want to be in, and to let me out when I want out.