Hope this info helps: as far as testing relativistic mass, it has been done in particle accelerators. Scientists have accelerated particles to very near the speed of light (>99 percent c) and have measured their masses. More precisely, they have measured their energy (E=mc^2, remember). Thus they have found that as they put in more energy, the particle accelerates less and less according to relativity.

On the subject of propulsion systems, taking a look at the following equation, you can see that for a given increase in velocity (deltaV), you need exponentially more propellant.

Mp=Mv*(e^(deltaV/Ve)-1)

Equations aren't always helpful, so here's an example:

Say you have a rocket that has a mass (Mv) of 100 kg, and the engine has an exhaust velocity (Ve) of 4,000 m/s. Your rocket is in low Earth orbit (V~7.5 km/s). You want to go 8.5 km/s, so your deltaV is 1km/s or 1000 m/s. According to the above equation, you need about 28.4 kg of fuel. Not so bad. Now say you want to go 9.5 km/s, so deltaV=2000 m/s. now you need 65 kg of fuel, more than double. With a deltaV of 4000 m/s your propellant goes up to 172 kg. So your speed limit depends on how much fuel you can carry. And carrying more fuel means you need more structural mass for the larger fuel tanks, so the amount of fuel you need goes up even faster.

Okay, so lets disregard relativity and see how much fuel it would take just to get to 0.1 percent the speed of light given a 100,000 spacecraft (just to be a tiny bit more realistic). If we used the same engine (Ve=4000 m/s), then it would take about 3.7*10^37 kg of fuel. Thats orders of magnitude heavier than the Earth!

Hope that helps.