I am reluctant to upgrade from Mavericks

You can do this quite safely if you have an external drive available, as well as adequate backup. If you don’t at least have a Time Machine backup, you should not upgrade until you do have one. Until you upgrade, you should be using a current browser such as Firefox or Chromium, rather than Safari, since they work with Mavericks and are current on security updates.

There are plenty of inexpensive external drives. Get one to be your OS guinea pig, and install a new OS on that. You could also use an app such as SuperDuper to clone your Mavericks drive to the external, and upgrade the clone: that will tell you exactly what problems you are going to have.

If you have only 4GB of RAM, consider upgrading to 8 if you want to run any of the more recent OS versions.

My vote would be for Sierra, of the ones currently available.

I think Sierra is the sweet spot right now. High Sierra still has some issues, some even caused by the latest update.

Sierra and El Capitan are still getting security updates. The updates for El Capitan will probably stop this year, but Sierra will be good for a while.

As always, a huge factor for you is how much old software and hardware you are carrying around. The more old software and devices you have, the more chance it will not work in Sierra and High Sierra so you might lean to earlier OSs. If your programs and peripherals are all recent, then it is better to upgrade to a later OS like Sierra and High Sierra.

Unless you already purchased it, Yosemite is not a choice. Likewise, El-Capitan is no longer a choice if your Mac is capable of running High Sierra. Sierra is no longer available either.

If your Mac is capable of running High Sierra, that's what you should be running. There are important security features in High Sierra that you should have.

Unless there is something already wrong with your OS X install, there is no real reason you should expect it to fail.

Check for application compatibility at roaringapps.com before you upgrade your OS and make sure you have a good backup.

Sierra is still available to download, How to download macOS Sierra - Apple Support just in case you don't fancy High Sierra.

I always like to check the compatibility of all my applications before I do any upgrade. Here is the web site that lists applications and which systems they will be compatible with.

https://roaringapps.com/apps

The 2 places I’ve seen recommended most to buy reliable RAM are below. I have purchased RAM several times, a MacBook Pro battery, and a hard drive from Other World Computing and have always been very satisfied with the product and service. They have on-line instructions on how to replace the RAM. OWC has also tested RAM above what Apple states is the maximum. I had 6GB installed on an early 2008 iMac supposedly limited to 4 GB and noticed an improvement.

Crucial

Other World Computing

Just my opinion but I found Mavericks to be the best OS yet and I have used them all.

How to get macOS High Sierra

You can try to download it at the link below. If it won't let you, then your only options are to upgrade to Sierra/High Sierra or find an older computer where you can download it using your Apple ID.

El Capitan

One option is to create a new partition (~30- 50 GB), install the new OS, and ‘test drive’ it. If you like/don’t like it it, you can then remove the partition. Do a backup before you do anything. By doing this, if you don’t like it you won’t have to go though the revert process.

Check to make sure your applications are compatible. PowerPC applications are no longer supported after 10.6.

Application Compatibility

El Capitan 10.11 Compatibility information

macOS Sierra 10.12: Compatible Apps

Also check to make sure there is a compatible driver for your printer.

Do a backup before installing, preferable 2 backups on 2 different drives.

Open Disk Utility, select your hard drive (step 1), then the Partition tab (step 2), and select the partition. Using the /// at the bottom move it up (step 3) until the size box decrease by about 50 GB. Select the newly created space and hit the + button (step 4). Name it something and select Mac OS Extended (Journaled) as the format (step 5). Select Options and choose GUID (step 5A).Then hit the Apply button(step 6). Download the installer from the App Store and when it starts, point it at the new partition. You might want to make a copy of the installer outside the Applications folder to avoid having to re-download it in the future. Once installed, restart with the option/alt key held down, select the new partition and reboot. Test away.