If you are looking for a ship that can do missions well with a good jump range and handle some combat the Asp is a reasonably good choice. It's got enough internal space for smuggling and well-placed hardpoints. The Asp does have disadvantages though in its reactor which isn't really big enough to let you get the best defense and guns possible so you'll probably end up running energy-lite weapons or compromising on SBs. It's also an easy target and isn't particularly well protected with shields though it has a decent hull.
For pure combat the Vulture is a much better choice though. Better average firepower, more maneuverable, smaller target, better defenses.
Above the Asp you'd probably be looking at either the Clipper or Python. The Python costs more but in my opinion is the better choice for missions since it can do medium pad landings and for combat it simply has more firepower and better defenses. Some people prefer the Clipper but I don't really favor it.
For pure combat the Vulture is a much better choice though. Better average firepower, more maneuverable, smaller target, better defenses.
Above the Asp you'd probably be looking at either the Clipper or Python. The Python costs more but in my opinion is the better choice for missions since it can do medium pad landings and for combat it simply has more firepower and better defenses. Some people prefer the Clipper but I don't really favor it.