Gabe, you're new to guitar and an Fm is not one of the easier chords. To play it properly, you should be pressing your first finger across all 6 strings at the first fret. (This is called a "barre") Then you press the 4th and 5th strings at the 3rd fret. If you do it correctly, all of the strings should ring clear, and none should be muted. You might visualize it as being the same as an Em, but you're moving everything up by one fret.
Barre chords are a hurdle that all beginners must master, but it takes time and practice. Playing them at the first fret is particularly difficult because physics makes the strings a little harder to press so close to the nut. Meanwhile, it's important to know that there are alternative ways to play most chords.
Here's a short lesson on chords. Chords are formed according to a formula which determines what notes they contain. I won't confuse you with the details, it's easy to Google "chord formulas", but most chords only need 3 or 4 notes to be "complete". You can scramble those notes around in any order, but they must all be there to make the chord. Since a guitar has 6 strings, a few of the notes get doubled.
An Fm chord only needs 3 notes: F, G#, and C. Those 3 notes are available in many places on the fretboard, and will be an Fm wherever you play them, although their "voice" may be a little different. Probably the simplest way to play Fm is by just barring the first 3 strings across the first fret....and not strumming the 3 lowest strings at all. Like this: (x-x-x-1-1-1) or you could add the 4th string on the 3rd fret (x-x-3-1-1-1)
If you want to emphasize the low strings, you could play just the 4 lowest strings (1-3-3-1-x-x) Do you see that these are just partial versions of the full barre chord?
Another way is to form a Dm chord, then slide it up 3 frets...again, only strumming the 3 high strings (x-x-x-5-6-4)
Yet another way is to go all the way up to the 8th fret (x-x-x-10-9-8) or (x-x-10-10-9-8)
On the 3 low strings, you could play (8-8-6-x-x-x)
All of these variations are called "inversions". Each one sounds a little different because they emphasize higher or lower notes, but all will "fit" when the music calls for an Fm chord. So keep on working on full barre chords, but until you master them, it's okay to use alternative fingerings.
Playing guitar since 1964