Mrsurrey,
a) Switching on when you come downstairs:
Option 1: Use the "Boot at time:" or similar line in your bios setup (usually F1, F2, or some other button on startup, look for a line saying "Press xxxx to enter setup" as you switch on)
option 2: In your BIOS setup (all ATX compatible mobos as far as I am aware, therefore almost certainly yours!) there will be an option along the lines of "Boot on Power" or similar, which means that when you switch your PC on at the mains socket, it will automatically switch on & boot. Simply combine with a 5 quid timer socket thinger from woolworths like you use to switch on your desklamps when you're away on holiday. I would suggest you set it to switch on the power 5 mins before you get up, and then switch off around midnight if you go to bed at a sensible time.
b) For browser/email - add firefox/IE to the "Startup" folder in your startmenu (if you're using windows! assumptions... tell us more!) Then simply make your webmail site of choice your browser homepage and tell it to remember you/log you in automatically (easily done on hotmail, am less familiar with Gmail etc etc)
c) Use task scheduler to run the "shutdown.exe" command when you're leaving for work.
(Full tutorial here:
Using Task Scheduler to schedule the computer to shut down and restart at a specific time)
This will quit all the running programs and shutdown your pc...
all assumes you're running windows!