If you want to try different flavours of sound eg drive, octave down, tremolo, chorus, phaser which can work well with different songs, then a budget multifx can be a very cost effective way to do that.
A Zoom B1-4 is an excellent entry-level multifx, offering an excellent built in tuner, plus drums, looper and headphones out for home practice.
Other budget multis e.g. the recently released Valeton GP-50 are getting some favourable comments from fellow BC'ers too.