With an externally enclosed hard disk drive, with power supply, you could
use a clone utility such as Carbon Copy Cloner by Bombich software; it
works free but is shareware. Also, there is another one out there I haven't
tried that gets good reviews, and has been used to make bootable OS X
system copy-clones on external hard disk drives. You run the computer
from these, and can use the Disk Utilities on the clone to prepare the
original computer HDD for a new installation; or weed out what you don't
want on the computer HDD, and move the original copy back in, re-clone.
Before you try & erase the original system after making a clone, be sure to
test the clone to see if it will work to run the computer. This is a working
backup, so if the computer HDD fails, you could run it from the external.
Some people get an external enclosure that can be used to set up the
new Mac OS X system or a clone, on an SSD; then transplant the SSD
into the computer. Be sure the SSD and other components match, this
is mentioned because there are hard drive data speeds, such as 1.5Gbps
3.0Gbps, 6.0Gbps, etc and the HDD or SSD should be similar.
The OWC site has some information on SSD to help set one up, and a
few videos linked on their site (or youtube) on how to replace & install
a HDD or SSD. Other info on how to upgrade. When a computer can
use more RAM installed, that's the least expensive upgrade in hardware.
You could swap the setup SSD out of an external enclosure used to set
it up, and put the HDD from the computer in there; if you get a suitable
enclosure. However for backups with plenty of space, the idea of using
a larger capacity external HDD with faster spin rate, and larger 3.5" size
hard drive support, to use with a power adapter. Partitioned, this idea
can be used with TimeMachine backup and also a bootable system clone.
However most of this requires some hands-on and learning. And after awhile
some or most of it can be easy to forget. A clone is not made automatically;
so that is something to do every so often. And the TimeMachine has its own
rules to read up on and figure out. The TM won't run your computer.
Good luck & happy computing! 🙂