Those speakers are fairly efficient, but they're going to work best with a lot of power. A receiver could work and it would be OK for home theater and casual music listening. You say you don't have the budget for separates. What is your budget?
A receiver usually is an all-in-one unit. It usually refers to something that has an amplifier(s), preamp, tuner, DAC, and controls video. It will decode surround sound input like DTS, Atmos, etc. It may also have a phono stage. They are generally speaking, a swiss army knife built more for home theater than high quality audio.
An integrated amplifier typically has an amplifier and preamp but no video or surround sound capabilities. It may have a phono stage and some have DACs in them. Integrated amps are typically 2 channel and purpose built for listening to music. They may have a home theater bypass function so that it can work in conjunction with your home theater setup.