Incremental and available space

Hello all,

Having in mind a scenario that I want to follow on my work for some databases I was thinking of the available space I will have when using a full and incemental backups.
Can someone help me on this:

Suppose we want to take a weekly full backup and an incremental every day what will happen to the 1st full backup when the second one will be taken since they will have a different date (I do not use the no-timestamp option).
Can I just delete the previous Full backup and all the incremental of last week when the new weekly full and the first one or two incrementals will be taken?
Any ideas on how to use the incremental and not run out of space?

Thank you all