I found it in a tweet and I was pretty sure it was photoshopped silliness but people were acting as though it was a real thing. I had to google to confirm what's what...
Teenage Engineering's tiny handheld TX-6 mixer offers an instrument tuner | Engadget
It also has built-in synth and sequencer capabilities.
When I started out I used a cracked copy of FL Studios and then pirated or downloaded free VSTs. That's probably the cheapest way to start. You can get a midi controller for really cheap as well. If you're wanting something more physical it really depends on what you wanna do. Is there a specific sound or workflow you wanna go for?