I assume you're receiving email to only one address, so that both your work and home contacts use the same address to contact you. If so, you cannot automatically set the
From field when sending emails.
But if you had two addresses for people contacting you, you could setup default From addresses. When replying to an email, a From address is chosen based on which address was used to receive the message.
Such a scheme means you would need to inform your contacts to use a specific address for work/home related emails.
You could use, say
firstname.lastname@example.org - anything after the
+ sign is ignored by Gmail.
Then enter your Gmail settings, and go to the
Accounts and import tab. Under
Send mail as add new accounts for
email@example.com. Take note of the
Treat as an alias option to get the behaviour you want.
Also see the official guide to using 'plus' addresses.