TAM is out of date and does not work well with latest BTS patch.

It maybe DOA
My advice to the Original Poster is to get Civilization IV Complete. This patches to 3.13 and includes both BtS and Warlords, as well as the base game.
Install two copies of BtS one at 3.13 and one at 3.17 (Downalod from Firaxis). 3.13 allows for TAM and Espana 1936.
Most other strongly worked mods are at 3.17, especially all the high-concept mods (FfH / Fall Further, Rhyes, Road to War, Fury Road, Planetfall) There's also a version of the original Desert War mod out there which has been upgraded to 3.17. It has a couple of flaws, but nothing that makes it utterly unplayable. 3.17 also includes the Mesoamerica mod from Firaxis, but this is a little disappointing.
Warlords allows for all the Warlords Scenarios, but also enables the Pirates mod and the Ancient Arabia mod, both of which are worth your time.
I saw that there is remake of the Sengoku mod from Civ3, but haven't downloaded this yet, so can't comment on it. There's a plethora of Medieval Europe mods out there, I'm not sure which is the "best"
Base Game mods. Aside from Rhyes, there's a lot of them and it's kind of hard to pick between them. I think Extra is a good place to start, as it only includes items from the original game, so the tech-tree and new units aren't too onerous. Overlord 2 and Thomas War add many of the more popular add-ons. Rise of Mankind adds a lot, but I personally found myself being overwhelmed when I played it. (Sometimes less is more) However YMMV, epecially if you liked Double Your Pleasure on Civ3. I've not tried Wolfhanze or WoC yet, so can't comment on them.
With CIV IV: Colonization out shortly, it wouldn't surprise if we saw other colonization variants such as Africa or Australasia, or other colonizing nations such as Portugal. Time will tell as to which is the best.