Not much, there's a bunch of gold panning starter kits you can buy but at the bare minimum this is what I carry.
-Antique pickaxe that's probably over 100 years old, $10 at a flea market
-Small shovel, $15 at Home Depot
-14 inch gold pan, $5 on Ebay
-Snuffer bottle to suck up the gold, $4 on Ebay
-Smaller garden shovel, $1 at Dollar Tree
-Vegetable strainer used to filter out larger rocks and put gravel into the pan, $1 at Dollar Tree. I only use this when finding a place to test pan, then I use the bucket classifier in
>>1467535 to dig the hell out of the place
-Collapsible bucket to carry dirt into, $5 on Ebay
Plus I also have the homemade bucket classifiers in
>>1467535 but I didn't spend anything on them and just made the classifier myself. You can buy more stuff sure like a sluice but I've been panning for so long now that I can pan dirt faster than a sluice can.
My total investment is only $41 and I already found way more gold than that. Which brings me to the most important thing you need though - LOCATION. You can buy all the equipment you want but means nothing if you aren't in an area that has gold. You need to do a lot of research first and find areas where you can pan for gold and expect to find it, always remember that people have already been doing this for hundreds of years and the areas with gold are already well documented. Google for public areas for gold panning, in some places in Commiefornia it's illegal to even pan for gold now.