Basically, the difference between the two is this: JPGs are a processed photo, using the built-in processing software from the camera, to produce a final photo ready to print or display. You CAN still alter them and process them further if so desired, and using the camera's controls you can manipulate how those JPGs are processed by the camera (picture controls offer color profiles, adjustable contrast, saturation, and sharpness)...but what you get is a fully processed photo. RAW files are just what they sound like - they are unprocessed - they come from the camera chock full of excess information with no processing applied at all - it's up to you to choose how much to process them...you can choose the 'defaults' of the RAW program you're using, which may be the defaults recommended by the camera, or you can use your skills to create the final result you desire. But you do all of it at the computer, rather than in the camera. You have much more leeway to alter or process than with the JPG file, but won't get much more out of it without the basic skills and understanding to do it.
Don't get too caught up in feeling like you need to shoot RAW to be a professional...you don't. Many pros and very skilled photographers choose to shoot JPG, and for some people it's the preferred or better choice. The more you get right in the camera, the less 'need' you have for RAW to alter or correct things. If you're an avid computerhead who loves time spent in front of the computer, then RAW can be an absolute pleasure and the preferred shooting method even if you do get everything right in the camera. If you enjoy the photography more than the computer, then bump up your skills with the camera and learn to manipulate your camera's JPG output and nail your exposures and shoot in JPG, that way you can spend minimal time in front of the glowing screen of your computer.
As for the Sony A300 - it isn't a super-strong low light performer, but you should be able to pretty comfortably shoot up to ISO1600 with very decent results. The Sony sensors starting with the A500 and up are excellent with high ISO and low light shooting, with much better noise control and detail retention, but remember too that noise is amplified by many things - are you using DRO settings in low light that can boost shadow brightness resulting in more noise? Are you underexposing shots in low light which will cause much stronger noise? Have you set the in-camera noise reduction settings properly so when you shoot in JPG you get better noise results, or are you using good noise reduction software on your RAW shots to pull out the noise?
There's no question you'll get a better low light camera if you move to a newer Sony model - you don't have to go for the new A65 - the A500, A550, A450, A33, A55, A560, and A580, all will do much better than your current camera - some of those can be found on closeout or used and give you an excellent camera with all the same features you like on your A300 (in body stabilization, tilt LCD, fast live view). But you can also get better with your A300, and should be more than capable of shooting clean ISO1600s and usable ISO3200s.
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 150-600mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony A6000 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses