Closing in on one full week of EVE Online play now and I think I've disabused myself of a few notions in regards to mining. First and foremost there are two principal ways of mining; the first being solo mining, where you mine and then transport the ore to a facility for storage. The second is to mine and use a partner to haul your ore for you to a facility. Solo mining is obviously more secure in that you do not have to rely on anyone else. You take no chance with a partner absconding with your ore, and you needn't share your profits with the partner either. But its also slower because of the travel involved. The second method of mining, called "jet-can" mining (Jettison Can) is less secure in that you have to rely on someone else for your transport. It also erodes your profits, but it allows for superior on-station mining time. Once you start mining you don't have to travel, and will only move from asteroid to asteroid.
Since I was new I had pursued the first principal method this past week following guides to mine with a Frigate until I could afford a Cruiser. The problem with the Frigate is that its cargo hold fills up so quickly--as does a Destroyers incidentally. It becomes tedious mining solo in either a Frigate or a Destroyer for anything longer than an hour or so and started looking for another alternative. What I discovered was I could mine with a level 1 industrial and avoid most of the travel all together.
Industrials are not mining vessels per se, and you won't be able to fit more than a single miner on any of them, but their cargo holds will hold a considerable amount of ore. You'll still produce roughly the same amount of ore per hour as with a Frigate or Destroyer with no breaks in between round-trips, but with a lot less running back and forth. Switching to the industrial gave me considerably more time to read, or watch a movie, or whatever while I made the same (and more) ISK per day. An industrial is, in my opinion, a good starter mining platform but not something that you will want to stick with over the long term. Ultimately what you should be training toward is a Mining Barge and an Exumer beyond that. Until you are able to purchase and properly outfit a Mining Barge you need to make a decision about which method of mining you really want to go with.
You can easily solo mine in high-sec space with a industrial, but it's boring work. It's also slow. By this point in your training you probably will only be able to fit a Mining I unit to your ship and can expect to mine around 430-440 units of ore per minute. Not a terribly good amount of ore, but for a beginner quite acceptible. Solo mining will mean you will fill up in about 70 minutes and will most likely be able to complete a trip to a station and back in less than a minute. It'll probably take you close to three weeks to train to the point where you can fly and properly outfit a mining barge. If you are fine with the boredom then by all means stick with the freighter. If you find that too boring; too slow; or want to do something a little more dangerous with your ship when not mining then you might consider using the second principal method of mining, at which point sticking with a industrial makes little sense.
The second method involves jettisoning your ore into space and having a partner pick it up and transport it to a station. If you are not in a Corporation and conducting mining for that Corporation, a partner will cost you ISK for the services rendered. You'll also have to contend with finding a hauler that is trustworthy. Ultimately once the ore is inside someone else's cargohold you have no control over what happens to it from there. If you do decide to take this route however, you will want to switch to a Cruiser at the very least. There are a a few Cruisers that are more or less designed for Mining or Cargo hauling and those are the Cruisers you should be looking into at this point. I for example, use a Gallente Exequror with Cargohold I expanders and four mining units. Every few minutes I jettison my cargo into a can. My hauler picks up the can every so often, and I rinse and repeat for as long as I feel like mining.
The second method of mining, as well as the better mining platform, will enable you to vastly increase your productivity and give you a ship that you can have some real fun with at other times as well.