I was having the same problem a few months back. The show i'm doing is very detailed and has a lot of 'little pieces' to the sets. So what I did to distinguish between props and set was all the big things (ie Table, chairs, couch) was set pieces and all the additional things (ie table cloth, pillow, blanket) were all props. My prop lists are also very detailed because, as good as my memory is, I sometimes do forget things and would rather not have to go back into the script and look for the scene, then the set. I also like to make my prompt book 'Bus Proof'. That means that, if I get hit by a bus and cant finish the show, someone else can pick up that book and start where I left off. Therefore it should be very detailed.
It's awesome too that you're thinking outside of what the script is telling you (ie table cloth). Yes, mention it in your prop list. It's easier to write it in than take it out later instead of not writing it in and having to put it in after. Therefore, if your director doesn't want a table cloth, then you'd just cross it out. What I try to do when I first read the script is go over the whole stage in my head. I imagine what it's going to look like and then nit pick at it to see what other props would be there that you wouldn't really think about because they're so simple. For example: a kitchen scene. You'd have your big props (ie counters, shelves, fridge, stove, sink, table and chairs) then you'd have your props (ie fridge magnets, pictures on the fridge, salt and pepper shakers, etc). I'd do each set piece one by one to make sure that I have everything. I'd then bring it to the director to approve it and if they dont want something, just simply cross it out!
As for your glass example, it depends on you. I know personally that I dont like to overlap items through the entire show. I'd rather have two glasses rather than just one. But, if you think you can keep track of the glass and not have one of your crew members or an actor mis place it, then go for it! Its really a personal thing. It also depends on your budget. If you can afford a few extra glasses then great. If you can't, then you'll have to make do. I also like to think about the material that these glasses are made of...what if one gets broke during a show? So I'd have a few extra on hand just in case (because...we all know actors...)
Like I said before, my prop lists are very detailed and I'll make a seperate line for each thing. So you're example was Glass of ice water. I'd put down 1 glass, water, ice. All in seperate rows on my prop list. Now, if that isn't what you want, then you can also make sub categories. For your big category, you'd have Glass of Ice Water. Under that with bullets you'd put what you need for it (1. One Glass; 2. Water; 3. Ice).
Prop lists aren't as easy as people think. If you can't think outside the box, and you just use the script for what it says to get then you're going to have a really hard time down the road. Lots of people struggle with prop lists...dont worry about it

For a last note, I can tell you from personal experience (since I love detail) that when I look at a really detailed prop list and theres a lot of stuff on it, I stress. Try to avoid that. You can do that by making the categories as I stated above.
I really hope this helps :S and good luck
