The lorentz factor is only 1.4 at 0.7c. The relativistic doppler effect would then be:
z= 1.4(1+v/c)-1
= 1.4(1.7)-1
= 1.38
This is enough redshift to push yellow into the near infrared and to make a medium blue into a medium red... One reasonable estimate of the intergalactic energy density is about 1.8 eV per cm^3. Let's assume a vastly oversized vessel with 25m^2 area in the direction of travel. 1 m^3 is 1x10^6 cm^3, so we encounter 1.8x10^6 eV per m^3 swept. With our 25m^2 surface, we sweep 4.5x10^7 eV per meter of travel. At 0.7c, we travel ~ 2.1x10^8 m/s. Neglecting some ramifications of relativity, we arrive at a figure of roughly 9.45x10^15 eV/s (*1.602x10^-19 j/eV), or 1.51x10^-3 watts (that's 0.00151 watts or about 1.5 milliwatts). I generate more heat than that by breathing, and these numbers are based on a velocity far exceeding 0.2c and a spaceship nosecone the size of a small building. Where exactly is the scary radiation coming from?
Matter is another story entirely, as even interstellar gas and dust will generate enormous heat through impact. For very small particles, it is likely that some form of ionizing beam (perhaps in combination with a powerful magnetic field) could be used to sweep out the craft's immediate path. Whether or not this would work for something as large as a micrometeorite (or worse, some big chunk of rock) is questionable. Either way some manner of electromagnetic funnel or wedge becomes necessary if only to avoid debris, and may as well be adapted to collect reaction mass.
As for getting up to speed, use your supply of antimatter to catalyze deuterium fusion. Keep your deuterium in the form of hydrocarbons, or perhaps as water ice. If that doesn't do the trick for you then bring along a good supply of transuranics and blast it with antiprotons.
The truly difficult part of such a trip is navigation. Even now, with our best technology put to the task, we still have unexpected collisions with space junk. Finding and avoiding all potentially hazardous masses along the flight path with enough time to avoid collision (and enough power to maneuver) is a staggering task. Even if you have a fuel scoop there is no way your scoop could deflect a marble at those speeds, let alone a rogue planetoid with a very low albedo.