I think the best computer to start off with is any spare one you have on hand that can pressed into service.
I am using a 2009 Mac Mini which is a core 2 duo.....nothing special. If you have an old laptop or small desktop, then this is a good start. A computer with an optical drive will allow you to rip CDS into your library.
Get yourself a good budget USB based DAC, such as an Audioquest Dragonfly (Black or Red), Schiit Modis etc., depending on budget.
Then play around with the software side of things. I use iTunes with BitPerfect. Try to find software that also allows you to use your iphone/ipad/ android device as a remote. This makes computer based audio a real pleasure.
Next, try to rip as many CDs, download or stream as much music as possible so you build u a music library.
If you want to commit to computer audio further, then you can look at a more dedicated type of computer and a better dac.
Most of all have fun.