I'm also thinking of HoMM3, but with a caveat : avoid having your main hero's army retread already explored areas to gather troops:
Your main army get its troops from towns and creature dwellings scattered about the map, and each week these places generate more troops (one turn = 1 day) which you are supposed to strengthen your army with. The main thing that is important here is that another 'courier' hero/heroes collect and transport these for your main army. If you remember that golden rule then the base game of HoMM3 (The Restoration of Erathia) is mostly easy. The real, and infamous difficulty of HoMM3 can then be found in the expansions (AB and SoD).

Disciples 2 is even simpler mechanically compared to HoMM3, and imo at least as good as HoMM3. However it's quite challenging right from the start.

Thanks to all, lots of suggestions here. I will have a closer look.

I also love Civ4. It can be a bit intimidating, though. There's lots to learn.

Pure strategy games like Chess, where you don't have to work about resource management, can be a good way to go, too. It's been a while since I played, but I believe Kings Bounty has little it's no resource management. Fantasy Wars/Elven Legacy, too, but it can get tough in later levels.

For resource management games like Civ4, I loved Warlock and Warlock 2. Very fun, turn-based, and very easy.

With Civilization IV, if you play at the lowest difficulty setting, you can just pick whatever looks cool to build/research, automatize some things and still have a good chance to win. From then, climb your way up through the different difficulty levels while you become familiar with the systems you had previously ignored (worker management, city specialization, great people generation, use of slavery, etc.)

A more simple but very good classic TBS game is Colonization. If you can get past the early 90s interface, it's a great and immersive experience and has fewer concepts to learn and master. It was my first strategy game, when I was just a kid, so I can say it qualifies for beginners. ;)

Panzer General II is perfectly suitable for new players. Strategically Deep but easy to use, orthodox classic but gamey enough to be a starting point to the genre.

I would totally not recommend Battle Brothers not HoMM 3.

Into The Breach is super fun, and easy to learn.
I've heard good stuff about Fell Seal, looked like FFT.

Indeed. Into the Breach is very recomendable for a new user.

Battle Brothers is a dream come true for any tactic fan but it is probably too hardcore for what the OP demands. The same with Old XCOMs.

And HoMM 3 is very appealing and popular. But we must recognize the game is very hard. I'd recomend HoMM 2 instead but it can be equally hard. Leastwise it is even more appealing than the third.

The Warlords series.

https://www.gog.com/game/warlords_i_ii

Warlords II Deluxe is a fun game. The rules are simple to understand and quickly to learn during the first turns. At the start of each game you can set the opponents and the difficulty for each opponent. It also has a hotseat mode. Another strong point is the Warlords II Scenario Builder. You can find several custom scenarios:

http://www.heeter.net/warlords/
http://www.heeter.net/warlords/scenarios/deluxe/

https://www.lysator.liu.se/tolkien-games/entry/wl2deluxe.html

A Dune Scenario:
https://www.gog.com/forum/warlords_series/frank_herberts_dune_scenario_warlords_ii_deluxe

This thread here describes how to install scenarios in Warlords 2 Deluxe:
https://www.gog.com/forum/warlords_series/how_to_install_new_scenarios_to_warlords_2_deluxe




The Battle Isle series.

https://www.gog.com/game/battle_isle_platinum

GOG has the Platinum Package (including Historyline: 1914-1918 (aka The Great War: 1914-1918)). The first Battle Isle was one of my first PC games which I bought. The screen is split in two, one half for each player. While the first player can move his units, the other can attack and vice versa. It can also be played in hotseat mode.

The package also includes Incubation. The player controls here a squad of soldiers to fight aliens similar to X-COM with puzzles. However, it can be very frustrating. *G*

For begginer i will suggest Invisible Inc.
It is not easy but the game is designed to be played multiple times and one playthrough lasts only few hours.
It focus on the core of turn-based games - thinking and planning based on tools and mechanics.

I won't recommend XCOM Enemy Unknown because of its scripted nature and if you don't know what triggers next wave of enemies it could be frustrating save-load show. (I have no problem with that but somebody who want to fill turn-based love could loose his will to play).

I've played heroes 3, 5 and 6 and all of them has levels where main enemy cheats too much. It is possible to beat "normal" way but it's hard and takes a lot of borring time. It makes a huge difference if you have a knowlege of strategies and tricks.

I would recommend to look at Expeditions: Conquistador and Legends of Eisenwald.

Hard West could be interesting too but I've heard that it is hard and lack of overwatch.

Turn-based games is very wide term.

Cause of this topic I've found Machiavelli the Prince, it looks great but it is focused on menagement/trading.

Stop pontificating and GET IT. Fell Seal is superb.

However, I will. And yes, I was going to point out that enemy wave thing as well, but I reckon that you get used to it and learn to work your way around it after a couple of bullshitty moments (and yes, it really does feel really stupidly fucking bullshitty the first few times it happens). Easy mode is reasonably forgiving, you can ease the pace on many missions to give yourself a breather, there aren't too many different types of units and enemies to juggle around, even the biggest maps are relatively contained and you can ignore you units' stats if you want. The DLC, Enemy Within, adds a couple of layers of complexity to the base game that won't be to everybody's tastes; it's best avoided for your first playthrough, especially if you're trying to get into the genre.

Braveland series, for sure.

Short, easy, and still fairly fun.

Just to report back: Thanks again for the many suggestions.

For the start I have bought Into The Breach (much fun so far) and Braveland (not tried yet, will be next).

I have "favorited" this thread and will definitely come back to it when I am done with the two mentioned games and still feel like playing this genre.

Before you go, I'd like to recomend you another good fantasy hex wargame, The Battle for Wesnoth. It is a fan made open source free game with very attractive visuals and streamlined features. You can download it for free on its web page of if you prefer under Steam client. It is a mix between Panzer General, Fantasy General (very recomendable as well, so take note of it and the sequel) and Warlords II and III. It is deep, lot of content and very good introduction to discover the genre

Congrats, it's an awsome game, as you unlock new squads and pilots it opens a lot of strategy possibilities.
Just a small tip I wish I knew from the start, watch those broken mountains or ice, if you see a glowing dot underwater or in the mountain crack, it's a time pod with a hidden pilot, it's the only way to get them available to play and 2 of the 3 are the most powerfull pilots. Detroy the mountain/ice and step into it.