Suggestions for Digital Audio Recorder

You can get all the things you’re asking for (in a general sense) with either home or portable. However, a full size unit will have a lot more features - they have more room for circuitry & connectors.

A portable can make live recordings in the field. If you want that, you need a portable. If not, you should get a home unit.

Sony makes great portables, with excellent A/D converters. 

Please look for a used Sony PCM-D100. Too bad Sony discontinued this reference-grade portable voice recorder. Amazon has them as new or used.

Another option is the Korg MR2000S.

I still have an Alesis Masterlink in my rack, which is actually quite a good recorder.

I use the Tascam DA-3000 to record DSD128.  It can also be used to record the output of another A/D converter.

+1 Tascam DA-3000

@chris_g 

I have a Tascam DA-3000 and it is a great unit, capable of recording up to 24/192 and DSD 5.6. Unfortunately it has now been discontinued. Grab one if you can find one!