I personally wouldn't sweat the service kits just yet since it's a home use machine.
But I wold recommend doing a capacitor kit on it while it is out.
And also going completely over the chassis looking for bad solder joints and traces.
That is a hard call to make.....these particular models can be a bit tricky, not the easiest to "learn" on if there happens to be multiple issues. Some of the suggestions I'm giving now would be where I would start, but that doesn't mean it'll absolutely cure it or if there are others issues. But then again....sometimes starting with the more difficult ones teaches you the best.
Decent soldering skills is definitely a must either way. It's not hard, just takes some practice. And you'd only need a cheap iron to get you started. (literally - I use a $10-15 iron all the time still)
And please read up on discharging the anode hole on the crt tube. Either way you go you will need to pull the chassis, discharging the tube will prevent any "shocking surprises".