Do not buy an ESR meter but buy a decent LCR meter instead. One that can measure at least capacitance (Cs and Cp) and D at 1kHz. It will be better if it can measure at 100/120Hz for very big caps and 10kHz for small caps too. Modern ones often have a 100kHz range and have a Rac mode and that is ESR at 100kHz. If that is usefull ? It can be handy for quick checks on caps in situ. The datasheets of most caps gives ESR at 1kHz (most times in the form of D but 1/(2pifC) gives you the reactance and D times that value is the ESR) At 100kHz they give the impedance and because the reactance is near to nothing for bigger caps you are left with the ESR (but that can be a totally different value at the working frequency. ESR is not a constant and low ESR is not even defined.
http://www.pa4tim.nl/?s=ESR for more about ESR or the ESR site from EEVblog member Krypton.
Measure caps in situ only as a quick check, do not trust it 100%. (compare it to measuring resistors in situ, if a 10k measures 1M it will be bad but if it measures 1 ohm it still can be good, there is just something parallel to it )
In manuals the technical part is often divided in a few parts. most times including something like
- performance checks
- calibration
- explaining how the circuits work
The first one is the thing you have to start with. It will tell you the problems. sometimes people think there is a problem but it turns out to be a user fault. Following the manual is better because they tell you how to set up the scope and test equipment for each test.
The calibration part often is doing the same tests but do not start adjusting things before you are sure the rest is OK.
Do not swap parts only because you assume or read somewhere they can be bad. You can make the problems bigger or damage hard to replace parts or the pcb itself. Caps are well known for breaking but 95% of the time these are inside (cheap) consumer electronics. Most of my test equipment still has the original caps. Only Tek exception was a Tek 2710 SA and 2 caps in a 7704A but in its defense, those where the only two not original caps and from some vague brand.
Work systematic, follow the manual. Check the schematics if you are not sure what they want you to do. Read what instruments you need for each step. If you do not have them or something similar do not mess around hoping you can do it another way unless you are 100% sure that you realy know what you are doing.
Follow the steps in order because adjustments often influence other parts of the circuit. So adjusting A can influence the magnitude of B. If you first adjust B it will look like A is bad. And if you then adjust A and forget about B because you think you have done that right you can be in for a surprise because now A and B probably are way off. And some things influence a lot of circuits. For instance a reference powerrail. Some rails are the "mother" and influence almost everything. If you adjust that just to make it perfect, you can make things overall worse.
So forget all problems until you are sure the PSU is 100% but always keep in mind a powerrail can look bad because of a fault elsewhere. That is why you first have to do the performance tests.
Repairing scopes like this is not easy. You often need lots of specialized test gear and a sound electronics knowledge.
But you can learn a lot from it.