I use a Rigol TS-815-TG spectrum analyzer frequently, and I'm confident you would be very happy with one. It's an incredibly powerful tool for component-level troubleshooting. Once you learn to use it with a probe to directly observe frequencies, you'll find yourself wondering, "How did I ever troubleshoot anything without this?"
I've been doing this for many years, and while a digital scope like the Rigol DS1054 is a great tool (its menu system can even display frequency), a classic analog scope still has an important place on the bench. I'd also recommend building a low-level RF pickup that you can connect to your scope or a frequency counter via a good quality BNC connector.
Speaking of other gear, you will get a lot of value from a very accurate signal generator. I have an older Hewlett-Packard 8647A, which is a deadly accurate, high-end unit that works from 250 kHz to 1000 MHz. If you can find one for a couple of hundred dollars from a trusted source, jump on it.
Finally, consider a good frequency counter. I have two on my bench and use them constantly. It's not necessary to have two, but it's very handy. Don't go too cheap on this item; the low-end models often lack sensitivity and struggle to maintain their accuracy.
Also don’t forget a good quality DVM Digital volt meter and if you find a nice VTVM Analog meter that would also be handy. I have a wide band B&K AC Voltmeter I use for receiver alignments this would also be good to have on the bench it can be a different model/brand but very nice to have.
I promise you will be quite happy with equipment from either Rigol or Siglent—they both make very good products.
Ok I’m done running off at the keyboard.