@Simon Templar
The AspX is a good alternative to the Keelback mining wise. It's not much more expensive when equipped and have a similar great view from the cockpit. If you avoid the docking computer and supercruise, it has decent space. I started core mining in an AspX, and that quickly got me going. If you mine opals, each ton of opal is worth 1.6 million CR, when sold to the right station (check at EDDB).
Something like this will get you on the way for 8.7 million CR, and with a little luck it will easily pay itself on the first trip:
A ship builder, outfitting and comparison tool for Elite Dangerous
coriolis.io
Edit: This build is "as cheap as possible", but you can upgrade after a few mining trips.
Watch some videos, if you haven't done so already, as core mining is complicated when you begin. I can highly recommend these:
Source: https://www.youtube.com/watch?v=JVqT8SHE9gc
Source: https://www.youtube.com/watch?v=xMZPQ-PSYgk
Source: https://www.youtube.com/watch?v=htdpct-6Mg8
2nd Edit: It might actually be fun to build myself one like above and see how much I can earn on the first trip. BRB...
3rd Edit: If you dare to, you can swap the fuel scoop with another Collector Limpet Controller. That will speed things up, because you spend a lot of time waiting for the limpets to collect the goodies.