I also began with radios and eventually moved on to TVs. The same basic methods are used, only TVs are more complicated and use higher voltage. If you browse the Restoration section in my website, you'll find various TV case studies that may be helpful:
http://antiqueradio.org/restoration.htm
None of those articles is about a TV exactly like yours, but they may help you get an idea what's generally involved.
I would not buy a CRT tester until you have completed your first TV project and decided that you want to do more.
Have fun!
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html