|Don't ask to ask, just ask|
No offense, but something about the tenor of your post rubs me the wrong way. Maybe that's what it's like in big companies, but I think I would have very different advice for someone beginning work at a startup.
Exude self-confidence and intelligence
If you're thinking about the image you're trying to convey, you have the wrong idea. I would recommend finding a way to make a positive impact as quickly as possible, preferably within the first two weeks. Quickly get a rough overall feel for the whole situation (mostly meaning the architecture of the system you'll be dealing with, and that means more than just the code), then pick something small to start working on and make sure you understand it well enough to make a valid contribution (i.e., don't avoid asking questions and then charge ahead to implement something that doesn't fit with everything else, or that will need to be ripped out in the nearish future). Ask as many questions as you need to in order to get the minimum level of understanding you need. It's far better to look stupid than to do something stupid. You'll be working with these people for a while -- any poor initial impressions will eventually be either confirmed (if you really are a loser) or disproven by your actions, and diving into something quickly is the best way to gain the expertise you'll need to succeed in the future. Even better, it'll get you the notice of people whose notice is worthwhile (and you can't identify who they are by the org chart.)
Try to fit in
Anyone at a startup who judges other people by their clothing had better be in the marketing or sales departments. Body odor maybe (hopefully!), but not clothing. For a technical position, it just means that people have too much time on their hands.
Fitting in, though, is still valuable. You need to try to become enough of an expert on some area of the system that your opinion will be sought, heard, and respected -- and not too much, or you'll end up doing all the work yourself. Or floating away, the proud ruler of your own little island that will become less and less relevant over time... Similarly, you need to be aggressive enough to get your concerns dealt with, but not so aggressive that you suppress others' voices. These are mostly longer-term goals, though. When first starting, just try to exercise one of your strong suits, so that people start to "discover" you as a valuable resource in some area, no matter how narrow.
Don't be late to work
True. But don't be early either. And early might be most people's notion of "on time". You want to have a good intersection with the people who actually matter and get stuff done, and unfortunately their hours are likely to be scattered around the clock. (And be aware that many people will shift their hours later to have some uninterrupted work time in the evening, so in the early days you probably want to err on the earlier side to avoid pestering them when they're least receptive.)
Don't step on any toes
Step on toes. Avoiding them is a sure way of becoming an irrelevant, expendable drone. But do it only when you need to in order to get stuff done, and be very aware of whose they are and why your actions are considered to be toe-stepping. Even (especially?) in a startup, people will be wed to their current ways of doing things, and frequently those ways will prevent you from getting stuff done (or require you to spend insane amounts of effort on working around something that lost touch with its evolving set of requirements.) You might be able to argue someone out of it, but there will be times when you just need to rip a hole in their stuff in order to make them see that it is no longer quite right for what you need. Just be careful to justify your need. And work more on demonstrating the problem than on redesigning their solution -- you'll be far more likely to turn their irritation into respect.
Be paranoid -- but only of yourself. If you're getting your stuff done, then there's no reason not to spend some amount of time reading news, or IMing, or whatever. But beware the traps! It's easy to find yourself on a Friday, looking back and wondering where the time went. Work hard to raise your own expectation of how much work you accomplish in a day.
As for employers spying on you -- huh? Sure, there's some amount of that, but I've never run into it where there wasn't a justification (bandwidth usage or whatever). If your employer really had the time and inclination in that direction -- well, what do you love so much about that job again? Oh, right, the steady paycheck. Still, if you stay there for very long, you're going to end up with that same sort of mindset, so you'd better be looking for something else NOW!
Cast a critical eye on your new job
This one is dead on. Be careful -- it's really easy to get too busy and caught up in your day-to-day work, and completely forget about this. You'll wake up one day and realize you're miserable, underpaid, and mind-deadened so much that you're stuck.
I don't think I'm really disagreeing with the OP, so much as giving a different point of view, one based on the startups I have been involved with so far.