Need help extending and boosting wifi signal

The optimal way to increase Wi-Fi coverage is to run Ethernet cable from the 2nd story to the basement and install a wired Wi-Fi Access Point (AP). This will provide the fastest speeds, too, because the Wi-Fi signal will be dedicated to serving clients and traffic will be transported back to the router using Ethernet.

Another option is to use Powerline networking in place of Ethernet. Powerline is not as fast as Ethernet but is usually faster than Wi-Fi.

If neither of these choices is doable, then a wireless extender is the last choice. There are single band (2.4 GHz only) models, and there are dual band (2.4 GHz and 5 GHz) models. All extenders have a basic mode of operation where they connect to the main Wi-Fi network(s) and broadcast their own Wi-Fi network(s). In this mode Wi-Fi speeds will drop by a minimum of 50% because the each band is performing double duty of receiving client traffic and resending it to the router. Speeds may also be further affected because the extender should, ideally, be placed where it can reliably connect to both the main router and clients. In your case, the extender may need to be placed on the 1st floor. A unit with external antennas will generally have better range.

Some dual band extenders, however, can avoid this speed penalty by using one band for clients (e.g. 2.4 GHz) and the other band (5 GHz) for communicating with the router. On Netgear's extenders, this feature is called FastLane. On Linksys, it's called CrossBand. I've read that CrossBand is more flexible than FastLane. Crossband is capable of dynamically using both bands (i.e. traffic from a 2.4 GHz client will be transported to the router via 5 GHz, and traffic from a 5 GHz client will be transported via 2.4 GHz).

If you opt to go for the wired Wi-Fi Access Point, it can be a little confusing to find one. Some, but not all, extenders can function as wired Access Points. Among Netgear's extenders, this includes all 3000, 6000 and 7000 series extenders. 2000 series extenders cannot function as wired Access Points; they can only function as wireless extenders.  Most routers can also function as wired Access Points.  Routers tend to be more expensive since they have additional capabilties that aren't needed in an Access Point. Given that you are looking for an economical solution, an extender is probably a better choice for you. You will have to decide whether you want a single or dual band extender; with or without external antennas; with or without FastLane; and with or without wired, Access Point capability.

I hope this helps.