Which Tube Tester

For a beginner, many of the simple portable testers are great and easy to ship. Many people like B&K or Eico. For simplicy, I like SICO (superior instruments) also. You shouldn't need to spend more than $100. These will test for shorts, tube strength/life and should show if any tubes have other issues. However, the little testers usually won't do enough to help you computer "match" tubes.
The sellor should be able to tell you which tubes it can test for. If they don't have the manual/tube guide, don't buy it. You need to have the settings in order to test the tubes. Some have the charts built into the units.

I bought a B&K 607 on ebay and it works fine for me. I think you can get them for $50 or less

Many if not all B&K are solid state which is actually a good idea and produced well into 60s giving you the options you want. I don't know if the prices quoted are for excellent working condition calibrated examples. You have to realize that there only a few guys left with any real experience working on these. Be very carefu there is a lot of pure useless S**t, sold on ebay. I found out the hard way. Spend the money!or borrow someone elses. You should IMHO buy it from a reputable dealer it's worth not throwing good money after bad. BTW I use a 800 Hickock which test only some of your tubes but is a very good instrument.