You both might want to take a look at the weather averages for Edinburgh. Keeping in mind that they are averages, and things could be different for her time there, what she wears will definitely depend on where she will spend most of her time. City? Tromping around the Highlands? On the cold, wet beach?
Layers seem to be the best option. The rain coat looks a little more on the fashion side than the practical side, but not from the description. The 3-in-1 has good options, but is more outdoors than city. I'd hazard a guess that you are an REI member, like many of us. You might also want to take a look at Eddie Bauer and some more city-esque sources. And yes, long sleeves are the best.
There have been some discussions on the forum lately about thermals. Many people recommend them. I've lived in Germany, WA and Cincinnati (one year when the Ohio River froze over). I have never worn them. The only advantage I can see is to use them in an emergency or as pajamas. Base layers or long underwear don't have to be black, white or beige. There are some cute tops that are more interesting than that and can be worn on their own, like these from Land's End, or these from Eddie Bauer.
About the boots. I wouldn't wait to get them there. She can try on some Ahnu Montara boots at REI and if they don't have a color she likes she can order them online. I swear by these and I think they are cute. They keep your feet dry and warm with the right kind of socks and also help with all the walking she will be doing over different kinds of terrain in wet and cold weather, which I'm sure is wayyyyy more than she does normally.
Since I only take carry-on (22" or smaller), I'm not sure what a "medium" sized suitcase is. She will do best if she wears her heaviest and warmest clothes on the plane, including layers, coat, hat, gloves and scarf. She may leave SoCal in relatively warm, dry weather, but she will appreciate having immediate access to warm clothing as she exits the plane at EDI.
She will be there for a long time and I'm sure she will want to buy local clothing, so I wouldn't pack too much. If she can wear wool, all the better. There are lots of washable wool options these days.
I have gotten lots of ideas and help from the Vivienne Files. The coordination ideas presented there can save a lot of money. The garments shown are usually too pricey and too formal for me, but it's the concepts that are important -- especially those shown under Packing and 4x4 Wardrobes.
Under the influence of the VF, I've seen the value of scarves, but I get mine at Target! From trips to Europe during cold and wet weather, I've seen the value of vests. From what I see online, there are a lot of them available out there now. LL Bean is a good source. Some of the best colors come from Land's End or Coldwater Creek.
Assuming that she will wash her clothes once a week like at home, she really only needs clothes for a week or so. She will learn to wear things more than once before she washes them and to do the wash when she runs out of clean socks or underwear.