Whats your goal? Do you want quality or just loudness? What's the purpose of having 5.1? Is it movies or just casual song listening? If it's only listening to songs, then a 2.1 would do a great job too coz not a lot of streaming platform provide 5.1 audio format.. Also playing music from a 5.1 with all the speakers playing without any calibration is going to sound bad.. However if your need is for movies.. An avr would be your best bet. If budget doesn't permit, you can add two speakers first and then increase as you feel the need.
Buying speakers individually and building the box will require lot of precision, measurements, etc. Also, you will have the calculate the vol of the box, if it changes the frequency curve of the speaker, if so you will need to eq it accordingly..
There are various websites that can provide you with the measurements needed for your box based on the speaker.. You can Google it.