The most common question I receive when people find out I work in IT is "Why is my home wireless so bad?" This is probably the most difficult question to answer, but I'm going to give it a shot. There are two options available, depending on how much you want to spend and how much area you are looking to cover.
Single or mesh?
For small houses without a lot of neighbors, the easiest thing would be to get a single router with wireless built in. This will most likely have antennas sticking out of it like some weird alien beast. The thing to look out for when buying these is that they tend to be overloaded with features that most people will never use. It's a good idea to get the best one you can afford and to get a brand you recognize. Netgear, Asus and Linksys make very good products for reasonable prices.
If you have a larger home or a lot of neighbors, you may want to upgrade to a mesh network. This is a newer category of wireless devices pioneered by a company named Eero and quickly copied by Google (Google Wi-Fi), Netgear (Orbi) and Linksys (Velop). These devices create a network amongst themselves, improving the performance of your wireless. They are easy to configure, and the feature I like best about them is that they will install updates automatically if you allow them to.
All mesh wireless systems all offer a starter pack with at least three devices, and you can add additional devices as needed. This makes it easy to add more devices if you find areas of your home that are not covered.
Those necessary features
For both types of devices, there are a few features I can't live without. Most of the new devices allow you to manage the device via an app installed on an Android or iPhone. For me, this is an important feature. If you are using an app to set up a device, it is usually much more straightforward than having to log in to a web page to set up the device. All of the mesh networks offer such an application, and some of the individual routers do as well. I would look for setup and management capabilities via an app.
The second thing to look for is the ability to set up a guest network. You want to be able to share your wireless with guests without them being able to access your home devices. You never know what people have done with their devices, and they may introduce something into your home network you do not want.
The third thing is the ability to test your network. This is an invaluable tool if you have any issues. Google Wi-Fi, for instance, allows you to test not only the wireless connectivity but also the connection between the devices and the Internet connection speed all through a single location. This means even if you are not a technical person, you can get a quick picture of how everything is working.
Finally, you need to make sure that either the devices update themselves automatically or that updating them manually is a simple process. You should not have to go to a website and download the firmware and then install that firmware on the device. That requires to much time and effort that most people will not make.
I'm not going to pick favorites, but I was very happy with the mesh network I implemented and the amount of trouble I was having with my kids and the wireless network decreased dramatically. I hope you have the same experience.