how awesome! if you are working part time remotely you need to be VERY disciplined to not squander time ( i would be DREADFUL at this).
i would recommend you keep a journal with what project you worked on and for how many hours. the company should give you deadlines/lists of projects so you know their number one focus. so many times companys have one idea of how long something takes and the workers have another. it is important to check in with your boss and advice him/her of your progress (even if they DONT get in touch with you as much as you think). depending on how far it is, it is also good to visit/show what you have done in person. people REALLY have more of an impact when they are standing in front of you.
and yes def def def SAVE. in north america there is advice given to ALWAYS save 10% and NEVER TOUCH IT until you have a real emergency. but most of us wrack up debt whether in houses or credit cards or whatever. north americans actually save the LEAST on the planet so you are probably ahead of the game.
honestly if you can learn to save money (and some of us are better than others) you will be so in a great position. the ideal of most people is to buy a home to live in as this is GOOD money to spend (as you save on rent etc and you have something to show for it when resale comes along). times flies so fast its insane. and learn if you have any work related expenses that are tax deductible in the UK.
this might be relevant
http://www.direct.gov.uk/en/YoungPeople/Workandcareers/index.htm
Starting your first job: what to do about tax
http://www.direct.gov.uk/en/MoneyTaxAndBenefits/Taxes/WorkingAndPayingTax/DG_10010555
Get a job, UK style
http://evolt.org/node/1650
Career Builder UK
http://www.careerbuilder.co.uk/UK/JobSeeker/CareerAdvice/Articles.aspx
Career Advice
http://www.learndirect-advice-dmr.co.uk:8080/dmr/index.jsp
Day one in a new job
Integrating into a team
How to make your mark
Probation performance reviews
How to tell if you’ve made the right move
http://www.learndirect-advice-dmr.co.uk:8080/dmr/index.jsp
First pay packet
How far will it stretch and what should you do with it?
Moving back home
It’s not ideal, but living with parents again could relieve unwanted pressures.
Clearing debt
Strategies for getting back in the black.
http://jobsadvice.guardian.co.uk/lifeandwork/0,,1177003,00.html
Firstly, try to get a good night’s sleep the night before.
Dress smart.
Arrive early.
Do your homework.
Know the requirements of your job.
http://www.accountingjobs.co.uk/career_start2.asp
i always think it is good to stay somewhat informed on HR issues
http://www.hrmguide.co.uk/