Default Backup & Restore

I've flashed my phone a few times before, but the last time I've done so, Titanium Backup decided not to work, so I had a newly flashed ROM but no data to go with it. I backed up everything on my phone once (by means of copying&pasting all of the folders) on my computer, but putting them back on my phone didn't do anything.

Now I want to flash again, but I'm clueless as to what app I should be using to back up my phone, and which app would make it possible for me to have my data backed up. I know it sounds a bit vague, but basically, I'm looking to back up my phone so that when I clear everything and flash it, I'd like to restore my apps as well as the data along with it (like high scores in games). Does anyone have any idea what I should do? I currently backed up my current ROM (Android 4.3 and HTC Sense 5.0) with ROM Manager (v5.5.3.7), but I don't know if I can use that back up since I'm looking to flash Android 4.4.2 onto it.

Any and all help is appreciated. Thanks in advance!


EDIT: And I have one off-topic question... Should I flash gapps before or after flashing the ROM? I flashed gapps before and after last time and it worked fine, but I'm curious to know what the correct order is.