Personally, I think it's a good idea to use two different browsers for what you might call 'business' and 'personal' use.

One reason is, browser add-ons.

These can 'enhance' your web browsing experience, but they can also communicate, unbeknownst to you, with the developer's website.

This came to my attention when I switched from Firefox to Chrome.

When you select an add-on at the Google 'Store' (most add-ons for Chrome are free, just like they are for Firefox), you are given a detailed accounting of the information it tracks before you install it.

The last time I checked, that was not true of Firefox add-ons; they just install and (quietly) do their thing, more or less behind your back.

Of course, if you don't use add-ons, this is not an issue.

Nonetheless, I would still probably use two different browsers, even if just to keep 'business' and 'personal' information 'separate'.

Webmail

If you are using a webmail service, such as Gmail, I would recommend making sure you logon and conduct your sessions under https instead of just http.

Secure sessions under https encrypt everything you download (read) and upload (send); ordinary http does not.

In addition to updating your bookmarks, https is usually an 'OPTION' or 'SETTING' at your email website, somewhere 'under' your ACCOUNT.

I would also recommend using at least two different email accounts (not just addresses, or 'aliases'), again separating 'business' from 'pleasure', at least to the extent practicable.

HTH