Like Herb (Guitarhacker) I recommend the small jump to the multitrack recorder like the full featured Tascam DP-24. Yes, all of the portable, battery units will provide you superior sound quality and they are intended to capture practices just like you need. But...

But reading your post it's clear you intend to advance to more complex tasks. You are better served to buy equipment that will grow with you as your tasks grow. You will not enjoy the limitations these portable units bring to your wants and needs until you've already spent the money. For you to get the same outstanding results you see in the product demo's recordings (which by the way are set up by sound engineer experts) you will have to use great care in where your musicians are placed in the room, you will have to eventually figure out what to do with the drums. Volume leveling will not be enough. Most groups end up recording the drums separately. The input configurations on some of the portable units can be very limited. They are essentially compromises to attempt to work efficiently in common situations only.

The 8 inputs of the DP-24 alone will be worth the cost difference. It will reverse the situation where your band has to set up and sometimes play to accommodate the recording device whereas with a multitrack, the recording device always accommodates the band. The DP-24 can also be used for your mixer. You can capture a live performance with each instrument panned, and leveled into a decent mix. The DP-24 can also accommodate importing multiple and individual BIAB RealTracks and midi renders to be used with your practices and recordings. You can capture each individual instrument with it's own input as the band plays together live rather than capture a live mix. That is much more suitable outcome because each instrument can be isolated for review.

A multitrack can capture those future recordings you will be using in your more advanced manner providing you the ability to have better than 'rough cut' demos from the start.

For capturing clean recorded tracks, a multitrack recorder will suit your needs and works just as effectively as any DAW. For the dollar investment, it is more than worth the difference you will gain in actual use over a portable, handheld, battery operated, fixed mic pattern recording device. At least I think so.

BIAB Ultra Pak+ 2024:RB 2024, Latest builds: Dell Optiplex 7040 Desktop; Windows-10-64 bit, Intel Core i7-6700 3.4GHz CPU and 16 GB Ram Memory.