Good and inexpensive might be mutually exclusive.
How many tracks other than drums do you need?
Recording drums properly can take a number of channels depending on the desired results. For drums, the minimum might be kick, snare, and at least one overhead mic, but when we do sound for bands we often use seven channels (regardless of whether we are recoding or not) for the drums.
The new Soundcraft ui24r mixer can record multi channel directly to a usb memory device. The model name is misleading, because it actually has only 20 mic channels.
soundcraft ui24r - Google Search
Once you have your raw multi track recording, you are not done spending time, (and maybe money) before having something that you will want to share with the world.
If you can get by with 8 channels you could search for what some manufacturers call a "field recorder" but good ones cost a good percentage of (or even more than) what a basic digital mixer costs. And you would need a splitter snake to connect it between your setup, and FOH mixer.
My best recommendation is to buy a Behringer XR18 for 600$.
Behringer X Air XR18 Tablet-controlled Digital Mixer
We use one when we can get by with 16 channels to do live sound, and we often record shows for bands with it too.
If you already have a mixer and are used to running your own sound, and you are using an analog mixer now, you might justify a digital mixer because in addition to being able to record, You can do multiple monitor mixes. And each person on stage can control their own mix too. You would need a laptop to record to. Either Windows or Mac. And a tablet, either Android, or iPad comes in very handy to operate the thing with from anywhere.
Post production is a whole other story. We do it with software that was sold by Sony called Sony Vegas, and we combine the audio with video we shoot with low cost consumer grade camcorders, and if we have good lighting, we can make very good promo videos for bands.
