We have AT&T Uverse for internet and phone and DirectTV for TV. I live in California and storms aren't really an issue where I am so I don't have issues with the DirectTV dish. I infrequently have a channel issue which usually resolves if I reboot the system and once in a while, I miss a recording (usually because I didn't realize that I needed to reboot the system). But that is generally rare and I have great success using my phone to remotely set up a recording, a feature that I wouldn't have thought I'd care about. I really like the whole home genie service they have. I have 2 DVRs and I can record all the kid shows on one DVR so that's all they see, but I can watch shows that I recorded on the other DVR from that room if I want after they go to bed.
If you check the DirectTV web page, they sometimes have specials for new customers, at least for the first year. Cost seems pricey for just about every cable/satellite company, but it really depends on what you want. If you want a lot of pay movie channels, it will cost you. I recently dropped some pay movie channels to get my price down as I found I wasn't really watching them.
As far as AT&T Uverse, we have had pretty good and consistent service for the internet. Every once in a while we have to reboot the router, but it seems like that is true for other services we have had. And I found we have had to do it less often than we did with our prior service (some local company).
But we do have phone issues. When they first set it up, there was some issue (can't recall what) and we called them out to fix it. However, when they fixed that, the noise on the phone line became terrible. We've just been too lazy to set up a time to call them out to fix it and we really don't use our home phone that much. So, just try out both the internet and the regular phone once it's installed before the person leaves (whether it's AT&T or someone else). Don't take their word for it.