When using PS CC, I use "Save as" the first time I save an image, and use the drop-down menu to choose the format. Then the computer/program will remember the format you prefer. My choice is .tiff because it retains all the information in the photo as well as all the layers and edits I have made. I only use .jpg when saving for use in social media, never as the final "best" version of the image.

LR is included in the Adobe CC subscription, and I use that for organizing my photographs and initial editing. After performing some edits in LR, I move the image over to PS for more changes. When I use "Save as" and choose a format, the image is saved in both the LR Catalog AND the files on my hard drive [the program also lets you specify which folder it will go into, or to create a new folder]. If you want to go back into PS later, and do additional edits, openthe image in PS from within LR and continue working on the "original". [If you did not close it, the image will still be on PS, and you can simply go back to it and continue.] When finished, or when pausing for a while, I will then use "Save" and the changes are applied to the image that is in LR [AND on my hard drive]. Because I have never used PS alone, I do not know if what I do will work the same without LR, but it probably will.

Actually, Lightroom (Adobe) will allow you to work on two computers at once if you have the basic $9.99 license. You can license as many as you would like over that and have all work. I have the basic license and my wife and I can work on our two machines at the same time, any time we want. I also have it installed on 2 laptops. If we attempt to log into either of the 2 extras, it will ask if you want it to log out of one of the others first or both of them. It really isn't an issue and I love being able to take it on my laptop with me. And I have NEVER had need to be on my home machine and laptop while out of town. In town I can just log out of the extra. Its no big deal.