Wow, glad you both are OK. What a scary experience to go through! And I think your reaction to the incident is very healthy and completely appropriate, fwiw. And you're a long way from alone in reacting that way - see
http://agirlandhergun.blogspot.com/ for just one example. Also see
http://www.corneredcat.com/ for handgun advice and basic information generally. Kathy is a mod here (pax) and her website is incredibly helpful.
Dave's suggestion to continue hardening your home against intrusion is a great one. Having a firearm or firearms is a necessary fallback, a "Plan B" if you will, in case your efforts to encourage criminals to 'de-select' your home for their attention fail. In case de-selection (clearing away hiding places provided by landscaping, appropriate lighting, especially motion controlled lighting, all doors and windows locked etc.) doesn't work, make your home sufficiently resistant to intrusion that criminals either give up and move on, or make enough noise in their attempt at entry and are sufficiently delayed that you have time to prepare to encounter them on your own terms.
Just owning a firearm is not enough, even if that firearm is a shotgun. In order for a gun to help, a person has to be capable and confident in using it under pressure. Pressure can make people do weird things sometimes. Dave says a shotgun should feel as familiar to the shooter as a body part, and IMHO that's pure gospel. I love shotguns, particularly 870s, and I've been shooting them for going on half a century now. Even so, Dave has probably dropped more shotgun shells than I've fired
. Listen to him...
IMHO one of the most critical things with a defensive shotgun is gun fit to the shooter. You didn't say which 870 you have, and there are several models, including a Youth and a Junior model in 20 gauge that are tailor made for smaller shooters. If your shotgun doesn't fit properly, chances are the stock is too long. A lot of shotgun stocks are too long for a lot of shooters. But that can be fixed, either by replacing the existing stock with a shorter one, or by shortening the existing stock. So if your shotgun doesn't fit you properly, Job One is to
make it fit.
You say you want to add a rear sight - actually, you're probably better off IMHO not complicating things with sights just yet. Shotguns are pointed as a rule, even when shooting at stationary or moving targets. Learn the basics of shotgunning first, and then, if it turns out you need sights, you can either add a set or purchase a spare barrel with factory rifle sights installed.
A good recoil pad can be a big help, too...
I'm another of those who is a strong believer in professional defensive shooting instruction. If you're close enough to get a session of Shotgun 101 from Dave, by all means do so. There are lots of people out there teaching these days, and good instruction will steepen the learning curve a lot. It'll actually save money in ammo costs and range fees in the long run as well. Take a look at
http://www.youtube.com/watch?v=FhgwHQCJwWw for an introduction to one of the pros out there teaching today. My own favorite shotgun instructor is Louis Awerbuck at Yavapai (
http://www.yfainc.com/), Randy Cain is outstanding too (
http://www.guntactics.com/), so are several others with a national and international reputation, it depends on your geographic location who is close by or who will be training in your area. But any number of local folks are very capable instructors as well. The big thing is to find a teacher and get started training and practicing.
Some other general things I'd suggest you read/study:
http://www.nononsenseselfdefense.com/five_stages.html - the whole site is valuable, but this part is priceless. Crime is a process, not just an event. It's important to understand that fact, the better to foul up the process for the criminal.
http://www.amazon.com/Meditations-Violence-Comparison-Martial-Training/dp/1594391181 - shooting is a marital art too, though many folks don't make that connection. And there's a LOT more important stuff in this book than just the difference in what the local MacDojo ("Would you like fries with your black belt?") teaches and what really matters on the street. This book is IMHO critical reading for anyone who is serious about self defense. If you want a sample of the author's writing, see his blog at
http://chirontraining.blogspot.com/ .
Take care and Stay Safe!