I think this advice is great. But, for what it's worth I don't agree with it all. I thought I'd mention those points. Feel free to disregard!
Caddy.
At most places playing with a caddy is going to make you look like a tourist. If budget is a concern, this is a good place to save as they are dear in Scotland. If possible, put the money toward a second round. Play the first round just feeling things out, and by the second you'll be fine.
Rain gear.
I don't think you need gore-tex or the ultimate in rain gear. I use my 10-15 year old non-gore-tex Mizuno rainsuit here and in Scotland. Works great, and I've never gotten wet. It's gotten a workout at times, as I actually like to play in the rain. And as mentioned, it's fairly easy to avoid serious rain, even on a tightly planned trip. This is another good place to save money as top of the line rainsuits cost a fortune. The new rain gloves that were mentioned before are an absolute MUST though. A double-canopy umbrella can be used in most conditions and is helpful but not necessary.
Shoes.
Two pairs are nice but not necessary. One pair that is broken in and known to be comfortable is a must. My last trip I played probably 45 holes a day for 2 weeks straight in one pair and was just fine. The other pair gave me horrible blisters the 9 holes that I wore them, so they were dead weight, and I didn't use them again.
Lunch.
Lunch at the club is one of the highlights, so I wouldn't skip that. Rounds are fast, as is lunch, so I don't think you should have too much problem fitting them in.
Balls.
I'd bring a good amount of amo, because the wind and turf can through off your game and some courses will have a lot of places to lose them. And, you'll be playing new courses every day, and you might not know where to play on the blind shots! You won't find balls all over the course either, like you can in the states. In fact, not SERIOUSLY looking for a lost ball will make you look like a tourist! You can always buy balls there, but by American standards they are VERY expensive.
Most of all, enjoy. It's not just the courses. The Scots have a love and respect for the game that is truly wonderful. And infectious.
Hope that helps!