Actually, most of what you say leads me to believe that Lightroom would be best for you. I think that you are having difficulties because the work flow in Lightroom is a lot different that PS. It's a bit of a learning curve, but once you figure it out, you might wonder why you ever used PS in the first place.

To get a larger view of your image in Lightroom, you can toggle the sidebars on/off by hitting the tab key. Also, keyboard shortcut L will let you toggle through "Lights Out" mode so you can focus more attention to the image.

For quickly narrowing down a set of photo's to just the keepers, Lightroom has several tools. There's more than one way to do it, but any photo's to be deleted just select the photo and use keyboard shortcut X to flag the image as a 'Reject'. The image will grey out and once you have all your rejects flagged, you can delete them all in one step. As for any images that are keepers, you can flag them as a "Pick" by using keyboard shortcut P.

There's a couple ways to help you compare images to narrow down your picks as well. Keyboard shortcut C will put you into compare mode, and keyboard shortcut N will enter survey mode.

Once you've done your edits and you're ready to send them off, select them all and hit the export button. Set the dpi/pixel count you want, and it will automatically apply it to all the images.

About why Lightroom does Import/Export instead of Open/Save like PS. In Lightroom, when you import a set of images, it just puts it in a catalog. Any edits you do will not actually affect your original images. This is a HUGE argument in favor of Lightroom. It will not allow you to screw up the original files. So this is where export comes in. When you are ready to commit your edits, you export from Lightroom. During this process, Lightroom makes a copy of the original, applies the edits, then saves them. Your original files remain untouched!