Yeah, pretty sure I'm going to CCU to an exploring ship from my Hull A...now I need to decide which one....
Well if you are looking strictly at stock dedicated explorers your options are:
315P - $5 upgrade, starter explorer, can map smallest jump points(the other ships may not be able to fit)
Freelancer DUR - $65 upgrade, additional range, sensors, crew and cargo capacity
Constellation Aquila - $215 upgrade, increased Freelancer benefits plus a rover and snub fighter
Carrack - $265 upgrade when available, the current pinnacle of exploration ships, increased Aquila benefits, may possibly be limited to mapping the larger jump points
If you don't want a dedicated explorer your options are pretty much any ship out atm. They may not excel at exploring but you can explore in them.