There are several things to consider, depending on what you want to do and how you want to do it.
FIrst, that link that @Raleit provided is very helpful in understanding the different ships, but I would suggest looking at a Procurer for a barge and working towards a Skiff for an exhumer. Those have the strongest tank, something that is very helpful for a solo miner.
Now, the skills can become something of a rabbit hole, again depending on how far you want to go. With a barge or Exhumer, you will want to work towards T2 strip miners for better yields, but to make those effective, you will need to use crystals with them. There is a different crystal for each type of ore, and you need refining skills to use said crystals, so that queue can grow pretty quickly. On the positive side, they will also help with your refining yield.
The other thing that you will want to train is drone skills, both for defense and mining, and that actually brings me to an alternative approach- instead of mining with a barge or exhumer, consider a mining command ship like a Porpoise or Orca. After the recent changes to how those work with drones, with the right skills and right drones a solo ship can meet or exceed what an (unboosted) barge or even exhumer can bring in-plus you have the advantage of a stronger tank and much more hauler space when solo. If you are with a friend in a command ship who will boost and haul for you, that is less attractive, but if they are not around, training into the command ship is an interesting and potentially worthwhile path to take.
One important point about that- I am not at all advocating command ships as a way to mine AFK. You are always at some kind of risk from gankers or NPC rats (particularly if you are using expensive drones), so the cargo space is not to be considered an excuse to be lazy, but rather a way to maximize m3/hr as you will not have to unload as often if you don’t have a hauler. Stay by the keyboard, stay engaged, and pay attention
Lastly, if you aren’t already, mining ships are shield tanked, so make sure your skills there are up to snuff as well.