You seem to misunderstand primary, extended, and logical partitions. An MBR disk supports up to four primary partitions. As that's limiting, one of these partitions may be configured as an extended partition, which can hold an arbitrarily large number of logical partitions. Thus, your belief that you have "...two logical partitions left..." is in error; if you've got unused space within your extended partition, you can create as many logical partitions as will fit in your unused space.
Before you start planning this out, though, be aware that MBR is on the way out. If your computer came with OS X or Windows 8 pre-installed, and perhaps if it came with Windows 7 from the last year or so of its reign, your computer probably boots with an EFI instead of a BIOS and uses GPT rather than MBR partitions. GPT doesn't distinguish between primary, extended, and logical partitions, and GPT supports up to 128 partitions by default. Thus, if you're using a recent computer, you might not need to worry about this ancient distinction. In fact, it's possible to use GPT on even older computers, but the advantages of doing so are slim.
As to a /home
partition, that's a matter of opinion. Mine is that /home
partitions are advisable on any but the smallest installations, because they help isolate user data from system data. This can simplify certain types of upgrades and system backups