Webmail

[#1]

Is there a way to leave 'some' emails on the webmail server or is it a case of leaving all on or downloading all?

[#2]

If you are using webmail, then all messages are kept on the server by default - you have to explicitly download/delete them.
However, if you are using an e-mail client (eg outlook), then setting up a POP3 account will download and remove from server by default, but can be changed to leave the e-mails on the server - it a a "blanket" setting, though, and deleting e-mails on the server is not so easy.
For what you wish to do, using an e-mail client and setting up an IMAP account would fit the bill. E-mails are kept on the server (and a copy downloaded for display when you open them) but you can "drag and drop" them to a local folder (in your client) or delete as you see fiy.

[#3]

Thanks my pc is poorly [black screen] so unusable and it won't detect a 2nd monitor. I use outlook normally. Today I wanted to cancel my MX5 insurance as I have sold it but the all the insurance doc's were sent by email and thus in outlook that I can't see. I had to phone them to get them to resend and it just made me wonder if I could selectively leave copies on webmail.

[#4]

With respect it sounds like sorting out your computer, backing up properly, and storing important email attachments in appropriate locations on receipt would be more beneficial than just altering your email settings.
Another way of achieving what you want - though it's only easy to effect if you have your own domain name - is to use email forwarding and forward incoming emails to two accounts - I use PlusNet as my primary account and Yahoo as my secondary one. That way if there are problems with one operator I can retrieve emails from the other.

[#5]

My backs up are sorted etc - it was just something that I thought of because of these particular circumstances and was only a general inquiry.