Accepting that there are lots more changes to come yet and plenty of new features, i think its rather premature to start worrying about rates you can make money at now. I just sit back and enjoy the game doing what i like. I'm in no rush to get to the biggest ships, and even when i have the cash, not sure i will get one.
I mean, what do you want in ships for those roles?
Exploration - As someone has just shown, the sidewinder is ok, although limited in slots. The Hauler or Adder are both great ships to start going on long expeditions with. Hauler has great range for its price. Later on a Cobra is good. You don't need to go any higher, but of course, when you have the cash, the Asp is the one you really want to get. Is there any need to grind to that early on? Hell no! It will come eventually.
Bounty Hunting - The small ships are good for it but the best early-ish ship is the Viper. Get this baby, get it upgraded, and you are sorted for most encounters. Plus its fairly cheap to repair. A bit later, you can upgrade to the Cobra if you want, although its debatable if its better. Its a little more solid and you can pack more gear, but the trade off is a little bit of maneuverability. Again, no rush or need to get a better ship, but ultimately the Python is probably the best ship for this, or an Imperial Clipper, although the Clipper hardpoint placement is dubious. Federal Dropship is also probably a good choice later. Again, no rush.
Mining - This is one where bigger is generally better, but you do need to consider getting attacked while mining. You either want good speed or ability to fit decent shields, good hull, and weapons. Fortunately, at least one option is available for most later ships. Early on, the Hauler or Adder are both decent choices. Cobra a decent mid sized ship for it. Since you are making decent money, you should be able to get bigger ships at a reasonable rate, so no worries about being too limited. You can live happily with a mid sized ship for a long time with mining.
Trading - bigger = better more or less here. You can avoid most combat (unless playing in open in highly populated areas where you might meet player pirates), but as pointed out, you can make money hand over fist with trading, so no issues here. This is really the only trade that really pushes you to go for a bigger ship.
Also, i'll give an honourable mention to one trade missed but is obviously coming, and that is Passenger transport. We have no details on what this is going to look like or the money to be made, but as I understand there is going to be a line of 3 ships (from cheapest to most expensive): Dolphin -> Orca -> Beluga. No idea whether this is going to have any danger attached, for example, are there going to be people after your VIP passengers, or will you be required to travel to dangerous systems? We can infer that such ships will be not so manouverable and perhaps lacking in defenses. It may be we haven't seen these missions yet because its going to require player cooperation, with a couple of wingmen along to protect your weakly armed and slow interstellar bus.
Oh, and one thing that we might presume is also coming is salvaging. But its something we will have to see what they do in terms of stolen goods from salvage.