You're good to set it up any time.
Brian and I are two of Timeshift's staunchest advocates or ambassadors because it has saved our bacon many times over.
Brian has recommended an external HDD, as does TS's developer Tony George, as you will also read elsewhere, including my recommended reading.
But we are not here to tell you to expend limited finances on buying something that you can do without for the short term. So your existing HDD is fine and has plenty of space for Timeshift storage.
I would first read, and once absorbed, follow, the guide at Linux Lite
and just make allowance for differences with your circumstances, eg no need to create a /backups folder or whatnot.
Under this approach, there is no need for partitioning, as well, because when you choose, in the Wizard Settings, /dev/sda1 - Timeshift will create a folder called
.timeshift (note the dot)
in your Home folder. It will take the first snapshot, and store it there.
Again in the settings, be sure to check the box/es under eg "Include All", this will take a full snapshot.
The first snap will consume about 31 GB, by the looks of the output from the df command.
Subsequent, incremental, snapshots will only consume a few hundred megabytes or a gigabyte or so, as determined by the nett increase in usage of updates installed, and any foreign software you choose to install.
See how you go, and ask any questions where unsure.