I imagine they can refuse a request, certainly for a port over a PICC, if they don't feel there's justification. But I don't know if they really would!
I have a mini port in my arm. Some people have ports inserted in their chest instead. I am not sure how they decide where to insert them. The surgeon asked me on the day where I was having it and I didn't know, so he decided. Now that I've had it a while, I think it would be better if it were on my chest.
The obvious pro of a port is that it is completely beneath the skin so there's no dressings, no need to cover it for showers, you can swim with it etc.
The biggest con is that very few HCPs are trained in their use. This has led to many frustrating A&E visits and hospital stays, with multiple attempts to get a cannula into my failing veins and everyone staring wistfully at my port wishing they knew how to use them. (This is why I wish it were on my chest, so that I could perhaps learn to access it myself!)
So personally, unless you are a keen swimmer or going to be having long term treatment, I'd be inclined to get a PICC line over a port. They are always ready to use and any nurse or doctor should be able to access it.
Of course, some people get through their entire treatment without needing to go to A&E or anything like that, in which case it would make no difference.
Another consideration is that port insertion is a bigger procedure than PICC insertion. Some hospitals do it under local, but others under general. I had mine under local and it was fine.
I'm sure I had another point but I've completely forgotten it.
Halfbaked you've been busy! I hope the sleeping tablets help 
I'm a bit behind with Christmas preparations too. I reckon we have a good excuse 
I need to go shopping, but my digestive system is being an absolute nuisance at the moment
I've barely left the house all week. I've decided to ask my surgeon to refer me to a specialist surgeon if he cannot find any solutions to my issues.