Transition from hard line to wireless

I am new at this and don't know all of the terminology so I will do my best at explaining the situation. So my house is fully hard lined. I have an linksys 4 port hard line router and am looking to transition this to wireless. Now the location of the router is in the basement and and I am worried that a wireless router located down there will not be able to send a strong enough signal to all floors.I guess my first question is, since I have a router already, is the best choice to add a wirless access point? or do I buy a new wireless router to replace the old one. Now I was thinking that the access point would be the best option and since I have a hardline already established, if I ran a hardline out of the router up to the second floor where I would then attach the wireless access point and hopefully have a strong enough wireless signal throughout the house. Will this even work and if so is it the best option?

Thank you in advance.