Try https://8bitworkshop.com/verilog to get started with dabbling

I do the vast majority of my work on xilinx and it's easiest to just use the built in simulator. It's free and supports vhdl and verilog. Most support just one. For lattice and microchip work I use what the tool provides which is usually a cut down modelsim or something

start here: https://github.com/YosysHQ/oss-cad-suite-build

The other commentator mentioned Verilator (which is indispensable in larger designs) but you may also want to grab Icarus Verilog too. It's a FOSS simulator and, unlike Verilator, is 2-bit and so it handles X ("don't care") and Z ("high impedance") signals. It's ridiculously slow compared to Verilator but the greater fidelity can be valuable depending on what you're trying to do.

Verilator is very good. It's faster than anything else, and it is free. The downsides are it won't stimulate encrypted IP blocks. And it doesn't do mixed language sim, so vhdl is no bueno.