I have pretty much the same requirement as the OP (to create one or more galleries) and I use Lightroom, which is ideal for the purpose.
I find the easiest way is to have a collection called "Gallery" (or whatever), and add whatever you want to the collection. Then I have an export preset called (surprise, surprise) "Gallery". This exports everything to a suitable image size to a folder where I keep my gallery stuff. I go to the Gallery collection, select everything (Control-A), and run the export preset. Job done.
Actually, I have multiple galleries for different purposes - just using different collections and export presets.
The advantage of this method is that you can keep the gallery of images in step with Lightroom. If I add images to the gallery, then I just run the export again (choosing "skip" for those that are already exported). Or, if I've removed a lot of images, I generally delete the export folder, and export all of them again.
As the others say, organising images gets more and more important as the number grows. I've around 67,000 images in Lightroom, but I use keywords whenever I remember, and normally use star ratings as a way of rating and culling. When I've finished editing, anything with no stars gets deleted.
Beyond that I use colour ratings for fairly ad hoc sorting, or keywords for anything that goes beyond one shoot.
Another thing that helps: use a consistent folder organisation. I use a folder per shoot (sometimes a folder for a set of several small shoots on or around the same date). I have a top level folder "Photo Album", then folders underneath for each year: "2014", "2013" and so on, then for each shoot a folder called things like "14-12-22 Christmas lights" or whatever. I keep the date in the folder name, in the order year-month-day, so the folders sort in chronological order.
The images get imported into the folder and stay there. In Lightroom, it doesn't make sense to have different folders for fresh imports, stuff you're working on, keepers and so on. Leave things where they are, and use keywords, collections, star-ratings etc for any other sorting purposes.
But whatever you do, be consistent.
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