Save money and have a more reliable network by not wasting money on a crimper.
The professional approach (for reliability, rather than cost savings, but it is less costly) is to terminate cables to jacks or patch panels, and leave the crimping of plugs to factories. Which is to say, if you need a plug, buy a patch cable. In many cases they cost less than two plugs, and they are tested at the factory.
Most jacks (not all) that takes a "punchdown tool" which generally costs far less than a crimper (if not, shop harder.) Some jacks are "toolless."
Assuming you actually have Cat5e, given the build date, you need jacks and/or patch panels that are Cat5e or better. Or better being Cat6 or Cat6a, which might be the same price as or cheaper than Cat5e (as Cat5e becomes obsolete) but probably not Cat7 or 8 that will still have a large upcharge for no practical benefit.
If you need more cables active than you have open ports on your router (the others on the modem may or may not actually work, depending on how that's configured) you need a switch at the central location with at least one more port than you have cables (since it needs to plug into the router to get your network, and that takes up one of its ports.) You can terminate the central cables to a patch panel, or to jacks that you mount in wall plates, depending how many there are and what your shopping reveals about relative costs for the number of cables you have. Use factory-made patch cables to connect the switch ports to the wall cables.
For a home-scale one-time project, the value of a pair tester is debatable, but they are relatively cheap, so if it makes you feel better, sure, spend $10 on one. You can also just verify that you get a full-speed computer connection across the cable, and where you don't you can carefully examine both ends of the cables to see if you mixed up wires, which is most of what a pair tester will tell you.
Pick one standard for termination order and stick to it. It does not matter whether that is 568A or 568B, so long as you don't mix & match. For whatever reason T568B is generally more popular. Follow the coding on your jacks and patch panels corresponding to the standard you pick. Most jacks and patch panels have internal wiring to make the wire connections on the jack or patch panel more sane than what goes on in a plug with crossed, reversed and split pairs.