Tagging and quoting is overkill, I heard you the first time!
As ever, here's a load of series, hope that one or more of them take your interest.
Bungou Stray Dogs - 24 eps including
its second series.
Shuumatsu no Izetta - Only 12 eps, but one of the better of last season's offerings, and certainly fits the fantasy and war tags.
Sengoku Basara -
Has two
sequels and
a movie. Aired after the switch to HD, and Production I.G. are one of the best studios out there, so the animation should be up to scratch.
Break Blade - A TV edit of
the earlier movies, so the animation is better than a lot of TV anime (and again, Production I.G.) I'd recommend the TV version over the movies though, as they added a few scenes.
Phi Brain: Kami no Puzzle - It would be wrong for me not to recommend this to someone who specifically asked for puzzle anime.
Has two
sequels.
Regarding age, all I can say is that I watched them all while over the age of 20, and liked the lot.
(Though I imagine Phi Brain could get repetitive if you marathoned it instead of watching it weekly like I did while it aired).