I got a different case form my D7000, the Case Logic SLRC-201 SLR Zoom Holster (Black) because it has a sling in it that suspends the camera so it doesn't beat itself on the bottom of the case, plus I can put my battery charger in it and it has a bunch of outside zipper pockets. It fits fine withthe 70-300 lens. The Evercase Grey case fits my D3200 with the 18-105 lens on it and the 70-300 next to it because the body is smaller. I preferred a beefier case for the D7000.
I'm going to assume you are talking about the Cannon Powershot SX510. After eyeballing a picture online of your camera, it looks very similar to my Nikon Coolpix L830 in size. I purchased this bag for my camera and I couldn't be happier with it. It had more pockets than I actually imagined. I can fit my camera, batteries and extra things inside the satchel. It has outside pockets which have come in handy when I want to carry just the camera bag without carrying extras (like a purse) but still need to have my ID on me. The most I have stuffed in this satchel at any one time was the camera, extra batteries, a pair of small binoculars (think opera style) in their case, a national parks passport book and I still had extra room inside for other things. I don't think this bag will support will hold multiple lenses (maybe 1 or 2) but if you have a point and shoot camera - it's unlikely you require a bag that can hold multiple telescopic lenses. I hope this helps you make your decision.