Agree to just try to learn a couple of songs anyway you can. Get familiar with your instrument and its sounds.
I started out with tabs, now moving slowly to figuring things out by ear and using lesser tabs. For me an advantage of learning from tab is that I'm automatically less inclined to look at the fretting/picking hand which is an advantage later on (IMO a player looks more 'free' and thus relaxed and thus interesting when not staring down at the instrument all the time).
To get a feel for the sound, which is more than just the correct notes, it is also about timing, volume etc. it is very helpful to play along with the track. Ben has now quite some lessons that include a video where he is playing the song slowly and the tab shows at the bottom of the video. This'll give you the chance to play by tab and by ear at the same time so it is very helpful to play along with those (and later on with the full speed version).
Speed comes with time, but in my opinion you have to practice it as well in order to get comfortable with it. Not everyday, definitely not when you are just starting out. Focus on playing correctly, clean and with good timing (metronome!), but once/twice a week you could challenge yourself by increasing the speed of the metronome step wise up to that point where you are just capable (or not) to play the tune. When I get to the point that I mess up the whole tune, I will play through it at a comfortable speed a few times to make sure the muscle memory stays intact and then move on to something else. Over time this will increase speed (be aware, you won't sound pretty), but be patient and don't focus too much on it. I'd say first focus on your 'groove' (and on clean/pretty playing) as the players who can do that are the once we like to listen to and to play with.