A covert ops ship should do fine. You should be able to fit most things you need for exploration on it, except for DPS. I wouldn't use a stealth bomber if you are planning on doing scanning and exploration, as the bonuses on a covops ship will make life much easier,as will the amount of mid slots for hacking/archaeology.

First, note that if you are cloaked, moving within 2 km of any object will decloak you.

The thing you need to watch out for in 0.0 (and W-space, to a lesser extent), are bubbles. If you're flying a covert ops ship that can warp cloaked, there are two scenarios in which you can get caught:

1. Jumping through a gate into an enemy fleet with a bubble up. In this case, you'll want to align toward a celestial close to the side of the bubble that you spawn on, then hit MWD and cloak at the same time. Keep spamming warp in order to warp off as soon as you get outside the bubble.

This will get you out 95% of the time, unless the enemy fleet has lots of fast tackle to decloak you, or yuo make a mistake.

2. Warping into a catch or drag bubble and getting decloaked by enemy ships/cans/drones. In 0.0, people like to set up bubbles in front of or behind gates, aligned with other celestials in the system, usually the other gate(s) that people will be warping from. They will set up jetcans and have drones out to decloak you.

To avoid getting caught in a catch (in front of the gate) or drag (behind the gate) bubble, you need to be warping to another celestial in the system before warping to the outbound gate. I do not recommend the sun or stations, as I often set up drag bubbles to catch from them as well. Pick a moon/planet/asteroid belt.

The other option for avoid all of this is to use a strategic cruiser (T3). Fit the covert and interdiction nullifier subsystems so you can warp cloaked and be immune to bubbles - you will be almost impossible to catch. This is a much more expensive option, though.

Lastly, if you plan to be moving through a particular region of 0.0 often, I highly recommend making on-grid tactical bookmarks (there are lots of other names for them). These are bookmarks 250-300 km from a gate, unaligned with any celestials. These will allow you to warp to a safe spot off a gate, observe it, then warp down and avoid any catch or drag bubbles. Don't make them any further away, as you might then be off-grid and unable to observe anyone on the gate.