TLDR:
TBS:
Kings bounty (+ expansion)
Age of wonders (Old but gold)
RTS:
DoW 1 (Multiplayer)
DoW 2 (Single player, and possible Multiplayer if you feel so inclined)
King Arthur - The Role-playing Wargame (Fantasy - Total war

)
Supreme commander 1 (the second coming soon)
Sins of a solar empire (Maybe as good as MOO 2, that's saying something)
Rise of legends (Superb under-rated gem of gaming)
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For turn based strategy, you can't get better than Kings bounty these days. Wikipedia it for its complete history but suffice to say the original laid the groundwork for the HoMM games. It also has an expansion that improves gameplay even more, though it does not make much innovation so try the original (remake) first to see if you like it.
Older TBS games worth trying are the "Age of wonders" series. Particularly the second installment. Good games from those times when you got serious gametime for your money.
On the RTS front I'd say that DoW 1 is good for multiplayer, but avoid it's single player campaigns like you'd avoid a shotgun blast to the head. DoW 2 is a complete overhaul game-wise, and it's kind of hit-miss. Either you like the style or you don't. I'd try DoW 1 first since it's more of a "classic" RTS
More modern games might include "King Arthur - The Role-playing Wargame", which is something like a Total war game but with fantasy elements. Do not let the name fool you, the only connection to the Arthurian legens are some place-names and characters. The rest is high-fantasy magic flinging.
Supreme commander 1 or sins of a solar Empire. Epic scale games that have a lot of tactical depth to offer a player. Supcom SP eats up quite a few hours of time and is well worth it (though a bit grind-y). Sins of a solar empire is for a more "expert" crowd. Since it lack a good tutorial or a campaign mode. The game itself though is brilliant if you are strategically inclined.
For "older" RTS games I'd warmly recommend Rise of legends. A game with genies, Aztec-inspired sun cannons and clockwork mechs. Can't get better than that.