You apparently have a unintentional radiator, so that means you don't actually have to have it tested. It is your obligation to make sure it meets the emission requirements if you sell it in the United States, but how you decide it does that is up to you. There therefore aren't any specs on what the equipment you use to test for compliance needs to be, since you don't have to test for compliance in the first place.
However, unless this is a very minor niche low volume product from a obscure company, it is a good idea to get it tested. Effectively, you can't do this yourself unless you are willing to invest 100s of k$ in a calibrated setup, and then spend a significant amount annually to keep it calibrated and verified. The test equipment itself is only the beginning. You need a proper range or anachoic chamber, calibrated antennas, etc. From the costs you were mentioning, this route is clearly not for you.
What you need to do, if you want to be really sure your device meets the requirements before you sell it, is to hire someone else to do the testing that has already spent the large sums on a proper setup. There are test houses all around that do exactly that as their main business. There are probably half a dozen within 2 hours drive from Boston, for example. I don't know what it's like in IN, but there are bound to be a few around. If you know what you are doing and have designed your device with emissions in mind, then testing may cost as little as $3-5k. The price goes up from there inversely proportional to how much you know what you are doing.
Your own test equipment will be useless for making absolute measurements, but it can give you some idea which frequencies you have spikes at. If you are careful to create a repeatable setup, then you can use it to test the relative effects of various changes to your design. For example, you might see you have a peak at 327 MHz with a arbitrary value of 20 dB with the way you arranged the receiving antenna, oriented your product, routed the ethernet cord coming out of it, distance from antenna, etc. After adding a few caps and series inductors to the power cord, you find the same setup reads 14 dB at the same peak. That means your design changes reduced that emission by about 6 dB. If you flunked formal testing due to that peak being 2 dB above the limit, you are probably OK.
Remember that your own tests are only for relative signal strengths before and after some changes you are trying to test. Repeatability of the setup is critical to get anything useful at all. When I'm doing this, I usually clear off a area, use a non-metal table, carefully tape down the antenna and the cord leading from it, and usually use tape to mark exactly where the unit under test is placed. I also usually tape down dedicated cords that go to the unit that are used only for the testing. Use other cords when running the unit elsewhere. The point is to not disturb the RF testing setup to that it is as repeatable as possible. This includes where you are while you are taking measurements.