The following is assuming you do not have a current backup in place. Also I assume that time is somewhat more important than money but not as important as having problems later.
For your immediate needs the MacOs setup procedure on a swiped or new Mac can import directly from an existing Mac (which you will want connected with the fastest cabling available to you). This will get you up and running quickly with a new Mac you want to look exactly as your old, and you can start working.
Then create a Time Machine backup using an external device (a USB3/Thunderbolt connected SSD would be a good suggestion) and good cabling. Either do this from your new machine (which I would suggest) overnight or your old one while you use the new one at work.
When that is complete, turn your old Mac in for service.
Then consider buying a Time Capsule (should still be available somewhere even though Apple discontinued it). The hourly backup is completely transparent and even if slow to restore, is still better than no backup at all (and somewhat better than a six month old backup).