I use ACDSee 2.32 for my image viewer, and although it has some annoyances I haven't been able to find anything better for a decade.
The feature I use a lot is the file browser, which is nearly a copy of Windows Explorer, which can handle file and folder copying, drag and drop, basic navigation keyboard shortcuts, and has optional confirmation prompts for file deletion. Slideshow options include highlighting a bunch of folders and files and telling it to "slideshow these". Jumping between image view and file browse is just one button (Enter).
I've tried Irfanview, but I don't think it had a file browser. I tried Picasa, and file browsing was okay(ish), but apparently the best and brightest minds at Google never figured out how to make opening an image full screen with no toolbars or buttons a one button action. The closest thing was to open the file, then start a slideshow, and pause it, which killed the deal. The last time I checked was last year, though, so if they've improved either program in the past 12 months that would be great.
The problems I have with ACDSee 2.32 are :
1. There's a Windows error ding whenever I use the arrow keys to move in the file browser, which I think started with Windows Vista or possibly XP
2. It can't open files or folders with Chinese characters, which prevents me from using it for work
Can anyone recommend something that works better for me?
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I use Windows Explorer and Irfanview, and I honestly rarely need anything else. With IrfanView, you can go through whole directories by using the space or pgdn key to view the next file, and backspace or pgup key for the previous file (and there's a whole bunch of other keyboard shortcuts.) There's a thumbnail generator for browsing within a particular folder, but I find Windows Explorer to work better in that case.
Also, Irfanview installs and starts up extremely quickly, as in, almost instantaneous. The only time it appears slow to me is when I open an image in a folder that has hundreds of thousands of images, because it takes a few seconds to scan the whole folder so it can report the number of images in the folder.
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Here's what it looks like: http://www.computers4seniors.org/images/irfan-24.jpg
Not sure if it has the slideshow option or the other things you are looking for as I don't use it much.