Part-Dieu is the modern TGV hub (faster trains, more connections). Perrache is older, downtown, walkable to Presqu'île.
Most TGVs from Paris arrive Part-Dieu. Allow 10 min walk + tram to Vieux Lyon.
The city has 2 metro lines, 5 tram lines, and a funicular up to Fourvière hill — get a 1-day TCL pass.