I used to watch plenty in the first half of 2000s, haven't really watched any lately.
I probably would still watch Trigun, that's one show I really loved. Short, but fun. It tells a tale about a really controversial gunman in a Western/Sci-fi setting in a perfect mix of humor and serious themes. With the exception of more serious episodes towards the end, the first half of Trigun (~ 13 episodes or so) is safe for I'd say most audiences.
Might contain spoilers - nothing that would ruin the series but might reveal some little things about specific episodes, at least the 2nd episode if I recall right.
The voice actors in the Japanese version are real great, I would watch it with subtitles if it's not too much of a culture shock.
Then I also have Neon Genesis Evangelion and Hellsing on my DVD shelf. I used to love NGE, but now I don't know. Need to watch it to find out if I'd still like it and Hellsing was cool because of Alucard. It's a very bloody anime though. NGE and Hellsing aren't for kids though due to violence and challenging themes.
NGE is half mecha battles and other half struggling through teenage years, angst and challenges in life. Despite having Evangelion in its name I can't recall any real Christian themes in it (a lot of themes like angels, Adam, etc in it though). Some legendary NGE AMV: