Calculating magnetic strength required to hold an objects weight + wind speed?

There are two questions being asked:

1.) How do I calculate how much force my electromagnets can exert

and

2.) How do I calculate the aerodynamic forces acting on an object that will be blowing in the wind, so that I can know how strong my electromagnet needs to be.

I'll answer question 1 first:

Just for future reference, the force exerted by an electromagnet is: $$F = frac{mu^2 N^2 I^2 A}{2mu_0 L^2}$$ where $N$ is the number of times your wire wraps around your electromagnet, $I$ is the electric current going through it, $A$ is the cross sectional area of your electromagnet, $L$ is the length of the electromagnet. $mu$ is the magnetic permeability of whatever your electromagnet core is made of, and $mu_0$ is the magnetic permeability of free space. This equation appears about half way down the wikipedia article titled "Electromagnet".

A couple of problems with this are that most electromagnets sold commercially do not state the exact number of turns $N$. Any number that they place on the packaging (if one is stated at all) is likely a rough estimate. Furthermore, most electromagnets sold commercially may state something like "iron core" on the packaging, but that doesn't mean it's made of pure iron. Hence, it is difficult to know for a fact exactly what the core is made of. This makes is more-or-less impossible to know $mu$, the magnetic permeability of the material from which the core is made.

The answer to question 2 goes like this. In principle, the aerodynamic forces acting on your "object" might could be calculated. But I guarantee you that this is beyond the scope of your project. Such a feat would require years of work by a team of engineers working full time. This isn't the direction you want to go.

In all seriousness, the best approach I see is to just trial and error your way through whatever it is you are designing.

Lastly, while doing so, bear in mind that many electromagnets sold in science kits are not very powerful at all. They are wimpy little things that barely exert any force on anything - it require a delicate touch to determine that they are exerting any force on anything at all. Be sure that you get something stronger than this. The strongest electromagnet I've ever encountered outside of a laboratory was the electromagnet that held the back door security gate closed at a restaurant I worked at many years ago. These electromagnets must be professionally installed and cost many thousands of dollars. Not to mention the fact that they can be quite dangerous in a wide variety of bizarre ways.

Best of luck with your project.