Help !

The easiest and least expensive route is to cull your CD collection.  Get rid of the CDs you don't actually listen to.

You should also consider a streaming service.

Transferring your collection to hard drive storage is not really hard, but it is not trivial.  It's very time consuming and you will have to build in sufficient safeguards to prevent data loss.   Plus, there's even a legal issue regarding whether you can dispose of ripped CDs.

Take to local Salvation Army shop, let them deal with them

Sorted!

Goodwill or the Salvation Army are good ideas. You must live in pretty small quarters though. I have about the same number of CDs, and 3/4s of them are on wall racks that hardly take up any space at all in my listening room. Are you being a little dramatic? 

@onhwy61 What is this "legal issue" you mentioned?  I think you may have gotten some bad information.  

schubert,

The easiest, most straight forward, cost effective way, that I know is the Bluesound Vault 2i. It is a single box solution, housing a streamer, hard drive and CD ripping drive built in. Just pop in a CD and it will rip it to the hard drive. Playback can be controlled from a smartphone, tablet or laptop. If you have a local dealer, stop in and give it a spin. It's a pretty elegant solution and the sound quality is pretty good.

Ripping 1500 CDs will take some time. I highly recommend you cull them and only rip the stuff you know you will listen to again. The Vault also support streaming audio, so you could also subscribe to a streaming service and stream music to you heart's content. However, the various streaming servers have different levels of content, depending on genre/type. Some services are heavy on current pop music and lighter on classical, and vice versa. If you decide you want to stream, post another question regarding the best streaming service for your listening preference.

Good luck and enjoy.....