5 will likely be the cheapest, funnily enough. You only need the final expansion, Tribes of the East, since it's a standalone. All maps and campaigns from the base game and first expansion can be imported to it (see here). If you get it on sale, it'll be as cheap as $2.49, and you can get it on Steam or DRM-free (bar a code for the online multiplayer) for that cost.

It's hard to say which one you'll like most if you're brand new to the series. 3 is generally considered the best, for good reason. 5 is on a similar level in general, though it's not as popular. Either are solid picks.

6 is... I just can't say a lot good about 6, honestly. There's no random map generator, and the number of maps available for the game is pretty weak. If you're running an unsupported NVIDIA GPU like I am, you'll likely run into frequent crashes with no hope of a fix, since the game's no longer being worked on. And, of course, a lot of peoples' biggest problem: UPlay. It also changes up the series formula a lot, some for the better, some for the worse. It's overall sort of a wash, and largely comes down to whether or not you like the changes. There's too much to go over, and a lot of it won't make sense to you since you haven't played the series before, so I won't go into it. Suffice to say, if you play 3 or 5 and expect 6 to be more of the same, you'll be really disappointed.

If you're looking to play multiplayer online, 3 is far and away your best option. The online for the rest of the series isn't nearly as popular as it is for 3. If you just want to play with friends or by yourself, any of them will do.

My recommendation would be to get 5: Tribes of the East, and pick up 3 when it goes on sale on GOG. Make sure you import the maps into 5 and get an HD mod for 3 (you can find links on the GOG forums).

Just do not get the recently released HD version of 3. It doesn't include the expansions, and so it's missing a ton of content and features, including a random map generator, a faction, and tons of maps and campaigns.