I'm considering buying a Sony Cybershot camera that uses memory stick. Would Ubuntu have any problems working with that format? Can I just connect the camera to my computer using USB cable to upload photos?
Yes you can connect it to Ubuntu with out any problems and It will usually detect as a Memory card that similar to Connecting your mobile SD card to Ubuntu system.
You can synchronize them also.
Here a list of best image viewers & by clicking it them you can find features.
No issues at all, I can connect my SONY RX-100 and RX-1 directly with Ubuntu and use Shotwell to download photos or take the card out and put it in the card reader of my laptop to read the photos.