First off, the best times to play online are during North American prime time, from say 4 pm to 10 pm U.S. Eastern Standard Time.
Unfortunately, for a number of reasons that go all the way back to the release of the game, this game just has low online player counts. The largest reason is probably that 98% of all purchasers only ever played it in single player and had no interest in multiplayer.
Player counts on the Sins/Entrenchment server seems to average about 35-40 during those times I mentioned. You will not see players who are currently playing games in the chat Lobby, only people who are not currently playing. The nice thing about the Sins/Entrenchment server is that you are more likely to find newer players there. However, it seems like most of the people only play against AI and not human opponents, so players are left to do 1v1's, 2v2's, and 4 man free-for-alls. Occasionally a 3v3 might fill.
It doesn't seem like too many people are playing Entrenchment now; I think that almost all of the Entrenchment people purchased Diplomacy.
The situation is a little better on Diplomacy where the average player count seems to be around 45 people. I did see the number reach 70 earlier this week. On Diplomacy you will find more people who are willing to play against humans. It isn't too hard to find 2v2's and 3v3's if you are willing to wait a little while. There are also a couple 4v4 games every night and sometimes a 5v5. It's easier to find and fill the 4v4's and 5v5's on the weekends.
So, the question becomes, should you spend $20 to purchase Diplomacy? I guess that depends on how valuable the money is to you and what you are looking for. If you want to play the game in online multiplayer against human opponents then Diplomacy is your best bet but I really don't know if it's worth $20 to be able to do that today. I mean, who wants to spend $20 for the privilege of waiting around for an hour hoping that a 4v4 will fill. Also, because you are a new player to this game, you will find that the game has a learning curve and that you will be absolutely demolished by the experienced pro players who know all the tricks and tactics and what players are likely to do. I'm not sure that's worth $20. I think you'll be better able to evaluate Diplomacy's value to you after you have played regular Sins online against human opponents for about a month.
Quite frankly, as much as I love the game and as much as I want to see it succeed, I really cannot recommend that anyone spend more than $10 on Sins or the expansions right now. I think that Sins itself is worth $10 if only to play it in single player and to play vanilla online, but it's hard to justify any expense beyond $10 now. I'd probably see things differently if I were one of the single player only people, but I'm online multiplayer against humans only.
Also, I am increasingly under the impression that Ironclad has lost interest in Sins and would like to wash its hands of it, as ridiculous as that sounds. I know that Stardock's people will deny this, but we have not heard (at least I think so) one peep out of Ironclad since the last patch and it almost seems as though they have lost interest and enthusiasm for Sins. I'm not sure if that should have anything to do with a purchase decision, but if it didn't discourage me from purchasing Sins and/or its expansions, it certainly wouldn't encourage me. It's really strange that Ironclad would not want to actively participate on this forum and keep fans informed about their current project(s), but that seems to be the case. It leads me to blindly speculate that there is some sort of a business issue or dispute going on behind the scenes.