answer for beginners, pls

this is very informative and helpful. thanks, spiritofradio.

You want cheap and easy, right?  But (i assume) you want decent sound quality (best possible on a small budget).  To the last part of your question -  bluetooth actually sounds better than ever now but still has its drawbacks, not just sonically.  There was a good response just above about a bluetooth receiver - you could go that route.  

I also assume that you have good speakers.  If so, hooking up a phone or computer straight to your amp will just not sound good.  And its not convenient.  I will also suggest to you that sending saved music over wifi directly from your computer or phone will not sound good unless you spend quite a lot on new equipment to fix the stream.  Further, your saved files would need to have been ripped into lossless format from your CD collection onto your computer, and, I’m just guessing given your questions, that you haven't done that. 

This means I’m assuming that an online music service will have the lion’s share of the music you want to hear.  Probably more than 80% of what you've collected and as far as what you don’t own (new music!) its almost unlimited.  

So, If you just want to play/control  music with your phone and computer over wifi and you're an apple user you can download a music app like Spotify, apple Music, or Amazon Music (i think all have both free and paid subscription-levels) and hook up an older model inexpensive apple tv to your stereo.  But, with apple tv you have to use a remote control too and stream over airplay (their own wifi system) and many people including myself don't think airplay sounds very good.  (Better off with new and improved bluetooth).

If you’re not an apple, or if you are and you want better sounding music than a phone over apple airplay can make, get the Spotify app for either or both your phone and tv.  its free.  If you want access to whole albums and more of your own choices get a subscription to Spotify.  maybe start with the Free version to get the hang of it.  Either way the only *other* thing you’ll need to buy is a Spotify Connect enabled device to hook up to the Auxiliary inputs on your old favorite amp.  There was one of these little devices mentioned above, Google Chromecast, but many people find that the sound it puts out (wIthout the help of other separate expensive equipment like a digital converter with a reclocker) to a stereo isn't very good.  you could sure try it - they’re only about 50 bucks (I have one I’ll mail to you if you like) - hard/almost impossible to make it work with an iphone.  There are many other better sounding little stand alone gizmos that work over wifi with Spotify.  There was a good one mentioned above for 200 bucks that also does other things.  There is one made by Klipsch (the big horn speaker company) that costs 40 bucks on amazon.  It sounds pretty great playing Spotify on its own (very much better than a chromecast on its own) and you don't need to buy anything else.  You don't need to use the software that comes with it except to set it up.  To play music you just use the Spotify app on your phone or computer, which is pretty good as far as these things go.  (My 87 year old mother just got turned on to Spotify and loves it.). spotify makes a direct connection from their servers over the internet, through your wifi network directly to your stereo. It takes your bad sounding phone/ computer out of it.  Its not lossless but it sounds really great and its simple and easy to use and doesn't require a big new equipment expenditure.  
As an aside, you may be thinking about Amazon music (it really is incredible) but its harder and more expensive (as of now) to connect to your stereo if you want to get the most out of it.  You can send it over Bluetooth, or Apple Airplay if you're an apple, but otherwise you have to use third party software because it doesn't have a direct “connect” feature like Spotify.  Others may disagree but I think as of now the need to regularly deal with third party software on top of the amazon app to make it work makes amazon music a little more complicated and its probably more expensive than using Spotify.  
So, Either 1). use itunes and/or apple music over apple airplay with your iphone/mac and a ($45 on ebay) apple tv plugged into the back of your amplifier.  Or, 2) use a music player and/ or music streaming app on your phone/computer and send it to a bluetooth receiver ($25 -$100 on amazon or at target) thats connected to your amp. Or, 3) get the music streaming app called Spotify and connect it Over wifi once to one of any number of spotify connect enabled little boxes ($35 -$500 on amazon or ebay) and again connect the box to the back of your existing amp.  
sorry, i think the discussions on here for the most part assume that we’re all using relatively expensive high resolution music files played through and on expensive gear.  I hope this helped to better answer your questions.   

Or an Apple TV if you are already in the Apple architecture and understand the limitations.  

Most economical and best sound quality is to connect the earphone jack on the laptop to the amp using an RCA adaptor. 

The Audioengine B1 works well, I use one to connect to a system in my garage but a less expensive option from a phone is a Chromecast Audio. They're no longer made but are plentiful on ebay for @$50. 
https://support.google.com/chromecast/answer/6279365?hl=en

The Chromecast Audio uses WiFi to connect and will give you better audio quality than Bluetooth but if you're sending lower bitrate mp3 files that might not be much of an issue. There are dozens of Bluetooth receivers on amazon or ebay that will let you stream from audio apps on your phone or laptop and provide analog output to an amp using a stereo mini to RCA cable. I've set up the previous version of this one for a friend. It's from a good company and works very well.
https://smile.amazon.com/TaoTronics-Bluetooth-Transmitter-Receiver-Simultaneously/dp/B01EHSX28M/ref=sr_1_2_sspa?crid=D60OCBMM6ILF&keywords=taotronics+bluetooth+receiver&qid=1571063575&sprefix=taotronics+%2Caps%2C183&sr=8-2-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUEzT1QyM0FXR0RNSEcwJmVuY3J5cHRlZElkPUEwMTg4NzIxMzI5TDU4OUM0QkhMVCZlbmNyeXB0ZWRBZElkPUEwMjc1NzM0MVEwUFlPVEJYRzc3TyZ3aWRnZXROYW1lPXNwX2F0ZiZhY3Rpb249Y2xpY2tSZWRpcmVjdCZkb05vdExvZ0NsaWNrPXRydWU=

Audioengine B1, works great, sounds great, and is easy to use. Has its own Dac, priced new at 199.00. You can get from Music Direct or a number of other places that will ship same day. Many reviews on line.