You can launch an Invite Only Session from the single player mode: select Options > Online > Invite Only Session. You can also choose to launch a Solo Session if you don't even plan to invite any friends to your game.

You won't be able to start GTA Online right from the get-go. That's because you'll need to complete the GTA single-player prologue first. Once you gain control of Franklin, you should be able to switch to GTA Online via the menu or by selecting it when launching the game.

Restarting your router is often the easiest and quickest way to resolve connectivity issues. Other bandwidth-heavy applications on your network can be detrimental to your ability to connect.