We have had two houses built in the past two years. The second one is almost finished. Everyone will have a different experience, but I can tell you about ours. Both houses were built by the same builder, but in different communities. Both communities have HOAs. Most of the homes have three different elevations (various differences in outside features) though some have has many as four or five.
In our case, many of the basics of the home could not be changed by the buyer. We couldn't decide, for example, to have the kitchen appliances installed after closing, or do our own wiring, or our own front yard landscaping. However, there were many, many things that we could change or upgrade if we wanted to. And that was fine with us, especially since neither one of us is at all handy when it comes to any type of do-it-yourself construction or renovating.
As far as options, we spent hours (and hours!) at a home design center where we could pick and choose paint colors, granite, flooring, carpeting, upgrades on appliances, cabinets, light fixtures, bathroom fixtures, and so on.
It was also at the design center that we sat with a wiring/electrical guy (I'm sure he had some sort of title, I just can't recall what it was) and decided things like hook-ups and wiring for outlets, phone and cable jacks, security systems, internet, ceiling fans, etc.
As far as asking questions, you're smart to keep a list so you don't leave anything out! You'll probably find that some things you won't be able to change, but there will be a lot that you will have options for. And you'll come up with many more questions each step of the way. Like others have said on this thread, I think it's important to think ahead to how you will use each room and where furniture might go. That way you can have your cable hook-ups where they make the most sense. We put cable jacks in every bedroom, the office, tv room, kitchen, and even one outside on the patio. We might not use them all, but they're there in case we do. We also wired for a wall mount tv in the living room and for direct tv.
Having said all that, I think the biggest piece of advice I could give to anyone having a house built is this: Visit the site of construction on a regular basis! I think it is so important to see each step of construction, not only so you can see the inner workings of your house, but to catch anything that might not be the way you wanted it.
It is SO much easier to catch a mistake and have the crew fix it right away, then to catch it further along in construction when it might be more difficult to fix. On both houses, my husband and I tried to visit the site at least twice a week. Sometimes we went more often, depending on what was being done to the house. When we went on vacation, our sales rep made sure to go to the house and take photos for us. On our first house, our sales rep even walked through the house and did a video for us!
We were careful never to bother the construction crew, and made sure to visit the site after hours. Toward the end of construction, when the house was locked up for the day, the sales office always gladly gave us a key so we could go inside the house to see what had been done.
By visiting as often as we did, we were able to catch a mix-up in the washer/dryer hook-ups, have a pre-wired fan box moved to a more central location in one room, have a dining room light fixture moved, and had a door (from the master bedroom to the master bathroom) put in where the builders thought there wasn't one. The builders also installed sliding patio doors instead of french doors in the most recent house. We told the construction supervisor, but he supposedly caught the mistake the same day we saw it. Either way, it was fixed at a point in construction when it was easier to fix it.
You've gotten a lot of good suggestions from people on this thread.

Congratulations on your new house! We have thoroughly enjoyed having a house (or two!) built! I have loved watching each stage of construction and documenting it along the way. Oh yeah, take LOTS of pictures! How could I have forgotten that piece of advice!
ETA: Many of your questions will be answered at your pre-construction meeting. We met at various stages of construction with our supervisor. We did walk-throughs after all the wiring was in place and before the sheetrock went up, then several times again before our final walk-through a few days before closing.