If you are worried about keeping it from being stolen I would find a way to store it inside, like FourteenEyes said it's easy to cut basically any bike lock or chain if you have large bolt cutters, people will even use battery powered angle grinders.

I'm not sure the size of shed you are considering but you could build something like this that doesn't take much space:

Even if it wasn't that secure it wouldn't be too noticable, you could cover it with a tarp or something too. That would still take a decent amount of money for wood, there are bike racks you could buy and weigh down with concrete but it seems like either a rack or box would take a similar amount of space and money.

A bike lock is to prevent a bike being stolen in public. Even the best ones can't compete with a pair of bolt cutters and 90 seconds of nobody watching them.

Locked to a handrail out in the rain

Assuming there's no garage or space inside to store it and that you have a back yard with fences to keep people from just strolling in, a concrete pad and some kind of stand or way to secure it might be your best bet. Probably looking at $40-50 in concrete for a small pad that's not going to crack and a couple hours of your time with a shovel and wheel barrel. Depending on how handy you are you could build a small roof or overhang so it's not deteriorating from the elements but that's at least another $100 in materials, and if you're going to that much trouble might as well build a cage around it to dissuade anyone from wanting to acquire it.

i know this isn't your question, but i hang my bike on my wall inside. leaving it outside, depending on the set up, is asking for it to be stolen eventually.

if i had some dinky 20-80$ bike i probably wouldn't mind locking it outside, although i still wouldn't.

If you go the safety route bucket full of concrete with embedded U-Bar is as good as you're going to get before screwing things into concrete.

But I'd advise the alternative; beater bike. Make it mechanically sound but look like shit so somebody elses bicycle gets stolen and if it does it doesn't cost so much

back when i had a bicycle as a kid, we always just left them at the top of our driveway near the house

then some kids stole them.. everyone got their bikes back except me.. never had another bike after that