I have 3 mixers. One is a tiny Behringer with 4 ins/1 out, and was purchased recently as a stopgap to mix a number of mono inputs from various pedals (my improv rig). I will likely keep it but plan to replace it with a Rolls Stereo Mini Mixer VI because that one has a separate headphone output (for monitoring practice, or recording live sets). No EQ, no faders, just 4 knobs. Sounds acceptable if I can gain stage to keep the levels below 5. Smaller footprint than any of my pedals. $25.
Second is a Mackie VLZ3 with 2 mic/inst pres with EQ, and a stereo in. It’s large for what it does (1 ft * 8 in footprint). I appreciate that it lets me use mics when I’m doing improv, so it might become my “acoustic” mixer for when I do live voice and contact mic stuff. It was $100.
Third is a Soundcraft EPM 6. 2 auxs, 6 pres, 3 band parametric EQ with adjustable mids. I bought this mixer to cover all my bases, and to be a small studio centerpiece. I can mix small shows on it, friends can come over and plug in for jams, and the routing is just advanced enough for what I need. I love it, it’s my dear, I won’t part with it. But it’s too big (for me) to tour with. I think I paid $175 new as a crazy deal on eBay.
To speak to your original post, whether I use a mixer or not for recording is dictated by my post-production needs. Do I want to edit/mix after? My interface (Motu Ultralight) only has 2 pres. So if I want to mix each channel/voice, I need a mixer to add more chans of pre so I can record each channel separately.
If I don’t want to bother with editing and I want to treat it like a live performance, I put all my inputs into a mixer, then into the interface. 2 chans, easy peasy.
Given what you’ve mentioned, I would find a mixer with individual direct outs for each channel. Plug each direct out into a line in on a multi-channel interface. That way all channels are line level at the interface, you get tactile control, and you can mix after.
EDIT: You only need pres for things that are quieter than line level - mics and guitars, etc. Synths are generally line level output, so you don’t need a mixer for them, only if you want to do live fades and EQ/fx adjustments on it. If all you’re doing is recording synths, you can skip the mixer and go straight for an interface with line ins. I highly recommend the Ultralight, my Mk3 has weird digital i/o problems but otherwise it’s amazing.