I used to live on Guernsey (from UK originally) and 2 months ago was offered a job on Jersey, but eventually turned it down.
It's beautiful and a lovely way of life. We absolutely loved our 5 years in Guernsey and spent many happy weekends and holidays in Jersey. However, there are some things to seriously consider.
As a student, even if remote, you will be an international student. Fees will reflect this.
Salaries and tax rates are very good and higher.
Cost of living however is very expensive. And extremely difficult on one salary. For example a standard 3 bed semi to rent starts at around 2300 per month.
Gas and electricity are expensive.
Health care and dental care is expensive.
Actually getting off the island is expensive. It's easy and transport is regular to UK, Guernsey and France, but it's very expensive.
There isn't much choice. No day trips in the car, long drives to see other towns, places etc. Once you've lived there 6 months, that's it. You've been everywhere.
I also found Guernsey quite insular and my friends who live in Jersey have said the same. Life and the outside world can pass you by.
I had an absolutely wonderful 5 years in the Channel Islands. 2 years of those were child free and the last 3 with my son.
We discussed returning as a family (hence the job offer), but ultimately, we didn't think it was right for our kids.
We look back fondly and it was great time in our lives, if VERY tough financially. But you need to think very hard and really look at the opportunities and options that your family need. If Jersey can give you these, then it can be fabulous. But if it can't, in my experience the compromise needed can be difficult and costly.