Refined from my general comment:
We don't need new physics knowledge to explore our solar system, whether the inner or outer planets. There's been considerable theoretical work on engines suitable for everything from Earth to orbit to Pluto and beyond. What you're referring to with most of a spacecraft's mass being propellant is the mass ratio: MR = (1 + lambda) / (epsilon + lambda), where epsilon is the mass of the structure divided by the mass of the structure with propellant, and lambda is the mass of the payload divided by the mass of the propellant and structure. The larger the mass ratio, the more payload you get for how much mass you're sending. So, how do we maximize the mass ratio? We choose engines with a high efficiency, or Isp (specific impulse). Basically, how effective an engine is at using its propellant. An engine such as a Hall effect thruster may have an Isp in the thousands of seconds, while an engine such as the Saturn V's F-1 has an Isp of about 304 seconds. The tradeoff there is that a Hall effect thruster has a pitiful thrust-weight ratio, and the F-1 has a high TWR. When it comes to intersystem travel, spacecraft have multiple factors to consider: launch vehicle, type of propellant, type of engine, destination, cost, availability of solar or nuclear power, and much more. In general, though, unmanned craft can afford long transit times with very efficient engines, while manned spacecraft should have a higher thrust to shorten transits.
Now, when it comes to interstellar travel, there are a number of interesting options. One is to take a large array of lasers, propel a lightsail to a significant fraction of the speed of light, and send it to another star system - with the proviso that unless it has onboard (and very powerful) engines, it will be unable to reverse acceleration in the target system and be captured by the star's gravity. Antimatter, if we could make it in sufficient quantities, would also enable interstellar travel in something less than a human lifetime. But if you want to go much, much faster, you would need something like the Alcubierre drive to make the trip, and the physics there is very theoretical indeed - we don't know how to make the exotic matter required, and that's one of the least of its issues. I don't see humans traveling to another solar system in this century as being probable, though certainly there will be humans among the outer planets once we build spacecraft such as argon-fueled nuclear electric ships.
You may find this table of engines useful and informative. The site itself is a gold mine of space-related information, so I hope it proves intriguing and helpful.