PVA unquestionably. Wallpaper paste will dry to a state where the wallpaper can be readily pulled off the furniture. PVA is used throughout the world in craft projects where a strong, reliable and resilient glue is needed. Neither of them can be regarded as waterproof though so I wouldn't put the furniture outside!
I'd recommend you Google the phrase "Elmer's Glue" for a good overview of PVA glue. Elmer's is probably the leading glue brand in the USA and it'll show you how versatile PVA glue is. There's no need to buy Elmer's as it's much the same as any PVA glue available in the USA. If you want to buy PVA glue at a rock bottom price, look at "No Nonsense PVA" in Screwfix (code 57248) at £9.99 for 5 litres. You can't get much cheaper than that and the stuff can be diluted to the consistency you want.