You get ONE wedding. Make it count.
So if you want to go to the courthouse/church in a gown and tuxedo, even if it's just the two of you or even if you only invite 5-10 guests, then do it.
A "wedding photo" occurs when two people who are getting married are photographed. It doesn't matter what they are wearing. A prince and princess who wear luxurious clothes to their wedding are no more or less married than a couple who goes to the courthouse in their jeans. A "wedding" is simply what happens when two people get married - location, formality, and attire DOES NOT MAKE THE WEDDING.
So, basically, wear what you want. Again, you only get one shot at a wedding (with the same person, anyway), so do what YOU want to do. If you want to wear a wedding gown, or a cute cocktail dress, or a pirate costume, then that's your right. You're still married at the end of the day, no matter what clothes you put on that day.
It's O.K. to have a private ceremony and then a larger party afterward. What is NOT acceptable is the opposite - inviting people to the ceremony but then sending them home afterward without feeding them. Whoever is invited to your ceremony must also be invited to the reception afterward. And a "reception" is simply the act of "receiving" your guests with refreshments and some gracious conversation. A big dinner and dance in a banquet hall, a casual restaurant meal, or cake and punch in the church basement ... all of those things are equally a "wedding reception."
However, please realize that if people are invited to your wedding celebration, then most of them will actually want to witness the wedding. Again, it's within your rights to have a private ceremony and then only invite them to a party afterward. But if your excuse is that you're too shy to invite them to the ceremony, then a lot of people might wonder why you weren't "too shy" to invite them to a party, where you will STILL be the center of attention. A lot of people might view it as a gift grab, even if you don't intend it to be that way. If you are truly too shy for a wedding with guests, then have a completely private wedding and don't invite anyone.
If you're having a civil ceremony led by a judge/secular officiant, or if your pastor is open to customizing the ceremony (a lot of religions have a set ceremony that cannot be changed, though), then work with him/her to draft a short and sweet ceremony. That way you aren't "in the spotlight" for too long.
Another option could be to welcome everyone to a party at a restaurant or a rental hall, eat and drink and socialize for an hour, and then stand up with your officiant and do a short ceremony, and then get back to the party. That kind of atmosphere might be a little more relaxed and informal, especially if you and/or the guests have a couple of drinks by that point.
If you really want the private ceremony followed by a larger party, though, it might be best to just do it on separate days. If you do it all on the same day, then people may feel offended that they weren't invited to the actual wedding. Get married by yourselves, or with a select handful of loved ones (and of course you need to feed them afterward, so take them to a restaurant for lunch or take them to your home for cake and coffee), and then have a casual family party at a later date. It's not a wedding reception since they weren't invited to the wedding and since your wedding day is over and you're no longer a bride and groom by that point - so wear regular clothes and don't do any special dances or cake cutting or anything.
One more point - I had similar concerns to you before my wedding. I don't like being the center of attention and I was nervous about walking down the aisle and reciting vows in front of all those people. But by the time everything happened, I wasn't really paying attention to any of it. I was zoned out and I just wanted to sit next to my husband and talk to him. Nothing else mattered. So try to relax.