“Lag” doesn’t have anything to do directly with frame rate. If your frame rate is too low, you will notice it - the game will feel slow. Lag is typically referring to latency, which is the time it takes for your actions to travel through the internet to the server and then be sent to everyone else. Basically, it’s the delay between when you do something on your end and when it actually happens in terms of when everyone else sees it. It’s measured in ping - the number of milliseconds it takes for a signal to get from you to a server and back, or the server to you and back.
If you play on a server near you and you have a good internet connection, you can get the ping time under 50 milliseconds, which is almost imperceptable for most purposes. Anything under 200 is generally playable without much problem - above that and it starts to noticibly degrade the experience. A few unfortunate console ports won’t tell you a ping, but rather will only give you a number of bars, sort of like cell phone reception. They think their users are too dumb to be able to understand “lower ping = better”.
As for the game… well, you’re going to get your ass kicked at first. There are so many people out there that are pretty familiar with FPS games that will have a huge advantage over you. I can only say not to get discouraged, and that you will get better. If you aren’t cutting it in straight up combat, there are support roles you can perform like being a medic or engineer which help your team without necesarily requiring you to have great aiming or movement skills.
As far as a tutorial or newbie servers, I’m not sure. I haven’t played TF2 in a long time. There tend to be some servers with strong communities, some of which are more adult and tolerant and helpful, but since I don’t play TF2 myself much, I can’t really guide you on how to find them.
I think the free weekend period ends sometime Sunday afternoon, so you won’t have too much time to play. I think the sale extends at least through Sunday, and possibly into Monday. So if you like it at all, it’s a good deal at $10.