What specs should I look for in a hobby milling machine?
Most hobby machine tools are made by a couple of Chinese manufacturers (notably Seig) and branded by the importer. However, while the basic machines are pretty similar the detailed specifications do vary and some brands will make a few key modifications and may provide more rigorous quality control. 

One thing to bear in mind is that, while you can do a lot with a fairly flimsy lathe, milling machines tend to need to be a bit more robust to be useful, unless you are only ever working with very light materials. 

There are a lot of very good hobby forums and blogs  which specialise in getting the most out of economy machine tools and these are well worth a look and often have long lists of modifications of varying complexity to improve their performance. 

The budget imported machines tend to be fundamentally sound but often lack somewhat in attention to detail in their design and construction so you can get a lot of benefits from a few simple mods. 

It's also worth pointing out that the machine itself is the bare bones of what you need and so it is wise to set aside a reasonable budget for tooling and accessories. For milling work holding is particularly important ie how you attach the work to the bed and things like indexible rotary heads can get quite expensive. 

I would also say that on this sort of micro scale for hobby work I wouldn't necessarily consider a milling machine to be essential and you can do a surprising amount (as well as achieving good dimensional accuracy) with good quality hand tools. 

So my advice would be to set up a workbench and start with a hand tools and learn what machines you really need. I would also recommend that you read this book despite the title it covers a huge spectrum of metalworking  techniques with an emphasis on basic traditional techniques.