I'm also not an audio engineer by any means, so I'm simply speaking from my personal experience in recording for school assignments and my own projects this term.
I'm not sure how to reduce the valve noise other than perhaps looking at replacing the valve felts (either those under the caps for upstroke noise or those under the buttons/on top of the valve caps for downstroke noise). But you might experiment with where, and how close you have the microphone to you when recording. Having it closer to you and elevated so that it's either above or level with your bell can help with the echo and reduce the amount of ambient room noise the mic picks up. (and of course, adjust the gain depending on your dynamic range for a particular piece you're recording to make sure the louds don't get distorted/clipped, and the softs are not lost)
In my situation, I've been either recording in my small apartment bedroom or in larger classroom at my university (very fortunate to have some limited access to the music building this term). The classroom has an air vent that's always running, so I've had to deal with figuring out how to reduce the amount of background hiss from that vent that's picked up on my mic (a Zoom H2n).
Willson 2900 TA-1 Euphonium - Denis Wick 4AM
Yamaha YSL-643 Trombone - Bob Reeves BrassArk 5G "Gladstone"
Yamaha YSL-8440 Trombone - Denis Wick 5BS
VMI 3301S BBb Tuba - Schilke Helleberg
Past:
York Preference 3067 Euphonium - Denis Wick 4AL
Benge 165F Trombone - Benge Marcellus
Wessex BR140 Baritone - Denis Wick 6BS
F.E. Olds Special Trombone (ca. 1941)