It sounds like Time Machine is now working ok for you.
I would also do the following:
(1) Try restoring one file or folder from Time Machine to make sure you can restore files.
(2) Consider adding a second Time Machine backup drive. Time Machine will try to alternate between them when you have more than one. If only one is mounted, it will use that one. Keep them both connected or if using a laptop, make sure to connect each one now every day or so to make sure each has an up to date backup.
(3) Consider adding a different type of backup, say a "cloning" program (SuperDuper, Carbon Copy Cloner and other programs can do this) which makes one copy of everything at the time of the backup. If done properly, the backup drive with these clones can even be booted from.
By adding different kinds and multiple backups, you are more resistant to a hardware failure of the backup media, or some other software issue that might interfere with restoring from a completed backup. Storing some subset of your very important files in the cloud adds another layer of protection (against theft, fire etc.).
Once you have your setup for backups done, you can just let them do their thing and be assured you are "covered."
This may sound a bit extreme but my experience is colored by my job where we do a lot of software and data analysis of data from spacecraft and redundancy in backups is mandatory. Also, eventually all hardware does fail. Because we keep computers running in our home until they actually do fail (I still have 2011 and 2013 MacBook Airs running, plus newer machines), we keep extra redundancy in backups. When the computer does fail, transfer to a new computer is very easy with these backups.
An example of why redundant backups are important might be a power surge that damages both the computer and the backup disk connected to it. Having other backups not connected protects against that.
