How can I learn to compose?

Don't get hung up on 'learning theory' or 'not learning theory'. What you want to do is gain knowledge about music, so you can use that knowledge to produce music. In the field of music, some of that knowledge tends to get packaged under the heading of 'theory', and some doesn't... but so what?

what aspects of music theory should I learn first?

Learning just a little bit of theory can be 'dangerous' - we get lots of people on this site who have read a bit of theory and get very confused. Partly this is because lots of aspects of 'standard' music theory arguably don't make much sense! The way music theory is commonly taught tends to mix up genuine music fundamentals, culture-specific terminology and notation, and style-specific musical advice into one big pot. Also, (as with most natural language), there are many terms that have rather uncertain meanings, or multiple meanings in different contexts, or different meanings to different people.

I'd advise you to learn as much as you possibly can, as quickly as possible, and not to get too hung up on any aspect. You'll probably need to go round it all quite a few times before it really starts to come together in your mind.

...so I know the notes?

There are lots of ways to 'know the notes'. You can know them as positions on a guitar fretboard, frequencies in Hz, dots on a score, midi note numbers, piano keys, frequency ratios relative to a root... ultimately you'll come to learn all of these ways.

time signatures

...certainly something you'll learn. Don't get hung up on them though... they're just one way of expressing a deeper 'truth' about music, which you will also learn.

or do I learn an instrument?

As the music you've said inspires you is traditional instrumental music, I would say yes, have a go! Try a few and see if any of them suit you. And if they don't, and you still want to compose, no problem!

Composition is something you can never fully learn - there's too much to know. At the same time, even a newcomer to music can pick out a pleasing melody on an instrument, and perhaps with a bit of trial and error, add an accompanying line, and come up with a pleasing composition. So it's going to be one of those things that is "a journey, not a destination".

Having said that, a composer IMO is someone who actually gets their pieces out there into the world! So while you may not feel that every piece is something you want to share, you may want to consider if you'd like to write for someone other than yourself - and if so, who, and how are you going to get your music into their ears? Writing music that no-one else ever listens to can be a hard habit to break.