@Eelco Scholten congratulations man!!! a few things that will help you successfully resurt this Honda Shadow barn find gem -
First, pull one plug from each cylinder and you can spray wd-40, or a few tablespoons of atf fluid in each cylinder and let that sit a few days. it will help lubricate the obviously bone dry cylinders. lean the bike side to side to let the fluid move around in there then hand crank the engine for a few minutes to lubricate the cylidner walls with the fluid.
when you do start the bike, there will be a considerable amount of smoke so do this with good ventilation, preferrably out doors.
While youre at it, replace the ignition wires, resistor caps and spark plugs, at the very bare minimum, replace the spark plugs, i do have an ignition tune up kit on shoptjbc.com and theres a video on how to use the kit on the youtube channel - https://youtu.be/_U0XheccdJE?si=jk3TFu6JQGJlzcAe
Next you will want to rebuild the carbs completely, however do not forget to replace the carb intake boots. they will not make a good seal anymore, once you pull the carbs out. we have the boots on the site.
Next, drain all the oil, and replace the oil filter and add new oil. i would run a full synthetic oil, i like royal purpole but theres many options.
next up is the coolant, drain your coolant, refill, and burp the system to get all the air out. the service manual details how to drain the fluid. replace the coolant with coolanol.
if the chain is stiff, i would inspect the o-rings. i highly doubt that chain is any good, youll want to get a 525-120 link chain and i like the clip master links, instead of the rivet links, theyre easier to change and service.
Inspoect those tires, any cracks are a sign of a tire that is not safe, and they should be replaced. last but not least - i would adjust my rear brake, and drank and refill the front brake master cylinder if you keep it.
Thats all i can think of for now! Happy chopping with that honda Shadow brother!