generally, you don't render to a movie file. Any avi or mpeg using compression codec, loses data, thats how it works. So the quality of the image reduces. You may not be able to see the loss in quality immediately, but to a trained eye, such as your potential employers, its obvious, and a sign of inexperience etc etc.
The standard method is to render your frames (see Render Globals) not forgetting to get your frame 'padding' right...i.e. if you have 100 frames of animation, you will render frames 1 to 100 with a padding of 4, so that frame 1 is named myAnim.0001.tif and frame 10 will be myAnim.0010.tif and frame 100 will be myAnim.0100.tif. The reason we use padding of 4, is so that any other software can read back the frames in the correct order. If you don't use padding, some software you use to playback the animation such as adobe premirere for example, will read myAnim.1.tif and myAnim.10.tif as the start of 2 seperate image sequences.
So once you have batch rendered your animation..which will take a while longer than a playblast, you will have 100 frames of rendered animation at your chosen resolution and quality. Now you have top quality renders that you can use to make your movies. So use adobe Premiere or whatever your chosen editing software is, to collate your image sequences into avi files or mpegs. Best not to use any compression codecs (uncompressed) so you have no loss of quality when it comes time to put your animation onto a video tape. This may take room on your hard drive, but if you were to make each animation for your showreel a compressed avi and then cut it together like most newby animators do, you will loose a great deal of quality with no way back without re-rendering. Also, it is hard to cut an avi into frames without loss of quality, makingit very difficult to edit and cut into showreels. Hence, you don't render to a movie file, you render frames, so you always have the best possible quality to begin editing with.
When your render has finished, you can playback your animation using fcheck for immediate viewing.
Also, you say "...without seeing the grids or animation paths"....I trust you have therefore only been using the playblast or hardware render buffer!!! The playblast is just an opengl quick-preview. It does not "render" your scene. I.e....if you have made a nice texture and a bump map for example, this will not render through a playblast. For this you have to "Render" (software render). ...again...see render globals. And remember, the images will render by default, to the images directory in your current project. So don't forget to make sure you have set your project or made a new one, before you render.
The playblast can record to avi if you switch the options. If you want a playblast preview render without seeing grids and animation paths...just hide the animation paths and go to the panel options in your window and choose show>grids (uncheck grid), and also switch off curves.