[u]Reasonable competence[/u] would be the more apt description of the necessary realistic [u]target[/u] level of skill to be acquired than "mastery".
Open F is a challenge for pretty much everyone starting out. [u]Multiple finger[/u] barre B is too, its difficulty exacerbated by shorter fingers and smaller hands. Open B is pretty easy as is the two finger barre B most guitarists including me use. But, it all takes time and is progressive in the learning and skill acquisition
[br]Can't recall how far F1 goes, but as I recall it covers all the common Open chords including those I'll mention in the paragraph below? If I'm errant on that, please forgive.
[br]With that salient in mind;
A. What type of guitar are you playing (i.e. electric or acoustic), and;
B. What kind of music/genre interests you that you would like to be able to play in future?
C. Can you play G,Em, C, D - C, D,G, Em and C, Am, F, G - F, G, C Am Open chord progressions fluidly with musicality yet? Both of those are pretty easy, common and solid progression finger trainers which will permit the playing of a zillion songs with rhythm, strum pattern and inflection adaptation.
[br]Use those and/or songs you like from the made easy songs or harder as you prefer selection here on GT or chord sheets elsewhere within capability of the chords taught in F1 as a tool to bring you up to speed if you self-assess either not comfortable with or not fluid with the progressions yet.
In conjunction, move on to Fundamentals 2 regardless, but keep working on all the salient practical material taught in F1 to achieve comfortable competency with it too.