I made this for my son to take to University. He said he liked greens, black and white with some brown in the mix. The colours I used are listed at the bottom of my comments below.
I wanted the blanket to be big and warm, and was surprised that the pattern used fine, 4-ply wool. I decided that any wool weight/hook combo would be fine, as the squares would be in proportion. My main concern was that amount of wool needed. In the end, I went with yardage, but part-way through realised that my squares would be bigger and hence need more wool? Doh! I had already made several of the sections when this dawned on me. To ensure that I had an even colour mix, from then on I made the biggest squares first, figuring that the little 2 round squares could be any combo with minimal impact on the colour balance. I really didn’t want to buy more wool.
As it turned out I didn’t run out of any colour, phew. However, if you are going to crochet join your squares, you will need a full, 100g ball to do it. I ended up using several slightly different shades of green, but I’m hoping no-one will notice but me .

Now that I’m finished I can appreciate that the success of this pattern is in the colour balance. I think that if the squares are simply made at random, the end result could easily just look messy and lack the coherence of the actual Babette.

I altered the pattern a little, making my own granny’s - I prefer to join the rounds in the corners because the join is less obvious, as follows:

I started off with a magic ring.
ch5, 3dc (US), ch2 3 times, then 2dc, join in 3rd of starting ch5. If I am not changing colour, then I join using a ss, if there is a new colour, I use the invisible join method.
Thereafter, if continuing same colour, I ss into corner space and ch5 to start, or started a new colour by joining new yarn in the corner space and ch5 to start. Each corner has 2dc, ch2, 2dc as the pattern.

Waaagh, ends and joining!!!
My advice, weave in ends as you go (I did).
I then started to join using the ss crochet method (randomly, part 7) but quickly realised that the best way was to work around from part 1. Join the squares of section 2, then join section 2 to 1. Join the parts of section 3, then join to 1 & 2….etc. I’m pretty sure that’s how the pattern tells you to do it, but I didn’t really get it until I started.
Also, when joining make the little squares into bigger squares first, then join with the next sized squares…..which means that you work towards long sides and fewer ends.
It has taken me 3 days to join, averaging 4-6 hrs per day. It is a big task but, honestly, it is so worth it.

For the border, I took the advice of Kathy Merrick and used a smaller hook which I think helped it not ripple.
It is very straight forward dc rounds. Again I joined my yarn in a blanket corner, ch5 then 2 dc in same space before dc in the following stitches. However, it is unclear what to do when you get to the corners of the individual squares (rather than the corner of the blanket). I did 1dc in the first corner where the squares meet, then 2dctog across the two and then a third into the second corner - hope that makes sense! As per the pattern I did 2dc, ch2, 2dc in each blanket corner.
I’ve included a pic of where the squares meet partway down a side so you can see how I did the first row of the border. By the time you get to round 3 of the border it is pretty much straight.

The colours I used are as follows:

Rowan Pure Wool Worsted - Ivory (101)
Rowan Pure Wool Worsted - Black (109)
Rowan Pure Wool Worsted - Apple (129)
Rowan Pure Wool Worsted - Mustard (131)
Rowan Pure Wool Worsted - Apple (129)
Rowan Pure Wool Worsted - Bottle (140)
Rowan Pure Wool Worsted - Aqua (156)
Rowan Pure Wool Worsted - Grasshopper (130)
Rowan Pure Wool Worsted - Hazel (128)
Rowan Pure Wool Worsted - Olive (125)
Rowan Pure Wool Worsted - Jade (127)
Rowan Pure Wool Worsted - Oats (152)
Rowan Pure Wool Worsted - Toffee (104)
Rowan Pure Wool Worsted - Moonstone (112)
Rowan Pure Wool Worsted - Garage (142)
Rowan Pure Wool Worsted - Cocoa Bean (105)
Rowan Pure Wool Worsted - Peacock (139)