Couple of removing branding, flashing questions topic

Hi, got an old S3 and I'm handing it down to my son. It's been a great phone and is still in perfect condition. It's currently locked to the Three network UK, but I want to use it on a different network (unlock it), remove the Three branding. (Flash a stock firmware) and I'm quite happy to leave it on 4.1.2

Branding: Three UK
MODEL: GT-I9300
AP: I9300XXEMD2
CP: I9300NELK2
CSC: I9300H3GEMD1
ANDROID VERSION: 4.1.2
BASEBAND: I9300NELK2
BUILD NUMBER: JZ054K.I9300XXEMD2

I have rooted several Android Samsung phones in the past and know the procedure (although can't get my Note Pro 12.2 wifi 4.4.2 rooted) :crying:

Questions:
1) Will flashing to a stock UK firmware unlock it to all networks?

2) Based the above information, which firmware would you recommend? When I look at the firmware section theres always seems to be several UK versions but none ever have my exact numbers on them.

Any help would be greatly appreciated.

thanks
Nemo