Ok here it goes. A network analyzer which is over $1000 is not required. All those will do is test for bandwidth and speed capacity. They'll give stats like near end crosstalk. They were popular in the days of Cat5 when every bit of speed was required and buildings network cabling were NordX or Belden certified. The building would get a certificate stating that the building was certified.
But for residential use a network analyzer is not required. The runs are rarely over 100ft and you aren't running wire above ceilings with tons of electrical wiring and fluorescent lighting. Our internet is also only 300Mbps max usually, with 1 or 2 connections simultaneously. 1000MBps is plenty for us. In large buildings you have 1000ft+ runs with lots of wiring and fluorescents and the people running the cables sometimes aren't the most knowledgeable.
In a house Cat6 is plenty. Cat6A will give more bandwidth allowing you to run up to 300ft. Cat6 will still give you 130ft or so at the same speed which is tons. With Shielded Cat6A you need shielded connectors. You need to terminate properly. Wrap the drain around the last pair and tuck it under the connector. Make sure you only untwist half an inch or so. I strip and untwist 3-4 inches or so, align all the wires, then clip them to 1/2" before shoving them in the connector. With a Cat6 connector and an insert you can shove the insert over the 4" of wire then clip it after and put the insert into the connector making it very easy.
As long as you have the right color code on every end which is 568B, wh orange/orange/wh green/blue/white blue/green/white brown/brown. The colors are left to right look at the connector with the clip away from you. You probably know all this already though since you already wired the house.
Just a simple continuity tester like you have is all you need. Make sure you have the right colors on each end and test for continuity after the crimp, you should be good to go. As long as you do a clean install with 1/2" untwisted max and don't yank to hard on the cable when running it. You don't want to pull tight and make tight bends, or leave a big loop all tied up for slack. Just pull the cable straight point A to point B, no slack loops for future use, no pulling tight, no super tight bends or kinking. It'll still work with these things, just a bit slower is all.