Yes one thing to note is that you can have a very small wedding in pretty much any registered venue, if you dislike your local registry office you could look at nicer ones elsewhere (a lot are in very handsome victorian town hall type buildings, it drives me a bit mad on these threads when everyone assumes registry office = brutalist concrete ugly building), or you can chose to get married in a small function room at somewhere like a hotel which is licensed for weddings, the latter will probably cost a little more but worth it if it feels more special to you. If you go for a midweek option the venue may give you a good deal.
Please don't worry about being too much the centre of attention or anything - the basic legal ceremony is very very short, you don't have to do customised vows or even the traditional ones about in sickness and in health if you don't want to - you just have to answer the registrar's questions about whether you are willing to marry, and repeat after them that you don't know any legal reason why you can't be married and the part about I Sue Bloggs take you Dave Smith to be my lawful wedded etc etc'. About 25 words total and you can say them quite quietly if you like, so long as the registrar can hear you. Then sign the paperwork. Even the most introverted people I know can usually manage that in front of their nearest and dearest without too much problem. You don't have to walk down an aisle, you don't have to be given away, you don't have to make any speeches or do a first dance or any of the other window dressing. You can of course do all the above plus perform a show dance dressed in spangly tights if you'd like to though, it's your wedding 
. The great thing about a very small wedding is you can pick and choose which elements you like and which you don't without disappointing great aunty ethel who thinks weddings without fruit cake are illegal or whatever. Or if you and your DH want to make some slightly more heartfelt/personalised vows or promises to each other you can do that privately to one another before/after if that' easier than doing it in front of an audience. I think it's nice to add some personalised touches even for a small wedding like some music that is meaningful to you (nothing religious though, that is not allowed in a civil ceremony), and perhaps to involve your children in the ceremony depending on ages, maybe they could read a short poem - again if easier you could do this somewhere afterwards, even outdoors on a beach or at a meaningful location to you?
Clothes wise again anything goes, at my registry office do I wore a pretty dress but not white and not a wedding dress, but if you want a full wedding dress why not, it's your wedding after all, you (hopefully) only do it once so who cares if you're over-dressed?
One of the best things about a very small wedding IMO is you can treat people to a lovely meal afterwards, I'd go for whatever you like best and is a treat - maybe afternoon tea or a lunch at your favourite restaurant?