Lightroom 5 has some excellent tools for removing unwanted stuff. Unless you are into advanced editing using layers photshop is not needed these days for most photographers.

It really comes down to post processing. If you want take your pictures and then be done with them except for printing, emailing or posting them online somewhere, then by all means stick with jpeg. The advantage with jpeg is that your camera will process the picture for you trying it's best to get the exposure, white balance etc. right.
On the other hand if you want to do editing and post processing to get the best picture possible, then you need to start with a raw file. This preserves all the originally recorded information so whatever software you are using can extract what it needs to give you the result you are looking for.
If you are unsure about this then most cameras that do raw also do raw + jpeg giving you both. Try this for a while and use the jpeg for quick results and use the raw file to try your hand at post processing.
Personally I use raw 90% of the time. But I switch to jpeg for times when presentation quality is not an issue. For instance I would use jpeg if I were taking photos to inventory items in case of an insurance claim.