Yes, there are better and worse cables. You should use solid core cables for running through the house. Avoid CCA cables (copper coated aluminium) at all costs.
Use the tool-less keystone modules which will fit the euromod faceplates and also into a patch panel. These will save you countless hours of terminating and re-terminating the cheaper ones using a punch down tool. Buy pre-made patch cables in various lengths rather than try to make your own using a crimping tool.
As it’s a new build, you may as well future proof and go for Cat 6e cables and connectors to make sure you can operate a 10gig network. The additional cost isn’t as much as it used to be. Motherboards, wifi routers and NAS devices are now commonly coming with multi gig Ethernet ports. If you are on a very tight budget, then Cat 5e will work just fine and may well support 10Gbe throughout the house if the cable runs aren’t too long.
Run at least two cables to each room, and at least 4 to any room where you are likely to have a home cinema setup. Even if some of these are just there as backups and not terminated, it’s far easier to run them all now, than having to re-run additional ones later when you are moved in, decorated etc.