Judith Tarr has a few degrees in history and writes some excellent action/adventure + plotty personal/political plotting historicals (both plain and fantasy-based) set in medieval and ancient/classical times (many sadly out of print). Some of them are available as DRM-free ebooks via
Book View Cafe and she's got some short stories to try out for free as well. I personally really liked her novel about Queen Melisende of Jerusalem during the Crusades (
Queen of Swords, one of the out-of-print ones).
Another primarily-fantasy author who did some very good history-based almost-pure-historicals with lots of warrior adventures in them is
Diana L. Paxson, who had some really good ones based on British/Celtic/Germanic myth and the actual times surrounding them (King Lear, Tristan & Isolde, the Nibelung part of the Eddas guest starring Attila the Hun). Again, severely out of print.
I'll give a tentative conditional second to
Morgan Llywellyn and
Guy Gavriel Kay mentioned above. I found their work to be somewhat uneven, with some books being very good and others being rather meh. But overall their quality and historicity are fairly authentic (when not being veiled with the fantasy element).
Of Llywellyn, I especially liked
Grania, about Irish pirate queen Grace O'Malley,
The Lion of Ireland about Brian Boru,
Druids set in the fallout of the ancient Roman conquest of Britain,
The Wind from Hastings about the 1066 invasion IIRC (maybe not specifically about that; it's been a long time since I've read it, but it's generally set around that time), and
The Horse Goddess about a girl from an early Celtic tribe who later becomes the legendary figure. TRB mentioned above is also a good one.
Of GGK works, my personal favourites are
The Lions of Al-Rassan and
A Song for Arbonne, the latter of which I admit is kind of an acquired taste. If I were you, I'd probably go with the Sarantine Mosaic mentioned above, which is also quite good (and avoid Ysabel; it's full of stupid people doing stupid things in a never-ending cycle).
If by chance you are especially interested in the Trojan War,
Glyn Iliffe's Adventures of Odysseus series is pretty decent. I wouldn't put it in a top 10 list of historical fiction, but it's reasonably engaging and the frequent battle scenes and political machinations are done well enough in the one book of the series I've read, IMHO.
Hope this helps, and welcome to MobileRead!