A lot has been said here about skills. Individual material / technique skills are important, and what has been said here is mostly true. But there is such a wide range of skills used in film production, it would be impossible to master them all, and even if you could, there are many "bad" or "tribal" techniques used in the film business that differ depending on the shop you work in. So when you work in a shop, they will likely have "Their way" of doing things.
But one "skill" that I have not seen talked about here, and is consistent in the film business, and it does not require college to learn. That skill is reliability. Don't be a flake.
Be on time, and be prepared to stay late. Be prepared to do dumb boring jobs. Then, do them well, and efficiently.
Don't act like you know something when you don't. Ask questions. Look up words you don't know (or ask).
Don't waste time. Time is most often the most limited resource on a film. I have seen obscene amounts of money thrown at a problem because of a lack of planning and lack of time.
I have owned and operated a prop shop for 35 years and the most common problem I have with new (or younger) employees, beyond reliability, is "lying".
I use this word deliberately, because they would not think of themselves as "dishonest" and in the normal sense, nor would I.
But, they lie to themselves and then to their supervisor about their skills. This is brought on by fear, fear of appearing stupid. (or desperately wanting a job)
When asked to do a specific task, they say they know how to do something and perhaps in their limited experience, they think they do know how. The results are often an inferior item, or worse, a ruined item and a loss of time.
It is difficult to "know what you know". Be honest with yourself, and the skills you have.
How to "Know what you know" or "don't know".
Educate yourself in what is possible in any skill set. Also learn how fast an item should take in that skill set. As an example, I can make (throw) pottery on a potters wheel. But I would not call myself a "potter". I can make something basic in 20 minutes to a half hour. But while at the Worlds Fair in Japan, I saw a potter making small vases in 15 seconds each. Now this is an extreme example, but you can get the point. What I can create in a 3d CAD program in 30 minutes a highly skilled guy can do in 5 minutes. But if I don't have that skilled guy, I'm happy with being able to get it done in 30.
Don't be discouraged, skills will come to you, and often in the order you need them. College is fine, but it may not be all that helpful, depending on what you think you want to do, and what you end up doing.
What props do you want to make? Is it really props you want to make?
The first question I ask a new employee (or interviewee), is; "What do you like to do?" I'm looking for the thing that challenges them, gets them excited. When people do what they really like, they will be better at their job.
So, What do you like to do?
Props? What type? Period props, Sci-Fi props? What materials? Wood, metal, plastic, fabric?
What about sets or costumes?
Is it the designing you like? Is it the building? or is it the problem solving and / or discovery of the process?
These are important questions to answer, and you may not know yet. But the answers will help guide you to the job you really like.
I never considered prop making back in 1979 when I started in the film business. Stunts, Physical FX and Makeup effects where the things I thought I wanted to do. I stumbled into prop making because I had skills building things, and I needed a job. Over about 10 years, I did all of them at different times, and eventually I found I liked the problem solving and use of different materials. This put me in specialty costume and props.
If you want to come to LA or NYC, understand that many bigger shops divide their work force into departments. Sculping, fabrication, mold making, casting, finishing, electronics and so on. So, in many shops, you won't get the opportunity to build a complete prop, just some aspect of it. This is why learning a set of skills to start your career, may not be necessary. Having experience in a range of skills is important because with the limited time we get to make things, understanding what the other guy has to do on the project, can help you understand what you have to do on the project. (and perhaps make their job easier)
If you are going to work in smaller shops, then you may be asked to do multiple aspects to a project. Then a wider range of skills is useful.
An important thing to understand in "prop building skills" is all of them are useful, and useless, depending on what you are building, who has what skills in the shop, how much time you have and how much money you have. Since many times props do not have real world engineering requirements, I can make a prop an a number of different ways, depending on the skills and tools I have at my disposal.
Problem solving is the most important skill in most jobs in film. A prop maker friend of mine delivered a light up "control panel" to the set and the Art Director loved it, but when John turned it on, the Art Director asked him how fast the lights could blink? John said "Blink?, No one asked me to have the light blink." The Art Director was furious, since this was an important part of the prop. Thinking quickly, John went to his truck, crawled under the dashboard, and yanked out the turn signal blinker and went back onto set and wired it in. The Art Director was happy again. John said to me later, "If he wanted it to blink faster or slower, I was screwed!" So being lucky is also essential.
Now while the structure of a prop is not always critical, the durability is, at least when it comes to filming it. I made the mistake early in my career of thinking, this piece looks cool, and even if it's a little delicate, I'll make it easy to fix. Well, you can't fix it in the middle of the shot when it breaks, and you can't fix a pissed off actor or director when your prop breaks. So it has to be durable and easy to fix. Also, it was mentioned above that props don't have to be completely detailed, you only "Build if for what the camera sees". Not true.
Example: The first Terminator film, was a low budget film, for an art director named Jim Cameron. The owner of the "Hand Prop Room" (Note: big movie prop company in LA) was friends with the prop master and trying to help him out. I was working in HPR's shop and had a few films under my belt and we where busy working on a number of projects in the shop, when we were told we needed to get some sci-fi props made for this little film. Everyone in the shop was already busy, so some of the people in the leather shop upstairs were enlisted to sculpt some props. They where not sculptors, and the resulting pieces where not very good looking, but we molded them and finished them since we had no time. Over the years, I had been told by many, "Paint it black, the camera will never see it". So we did.
My boss took the props to the set, and Jim Cameron took one look as these sorry looking props and chewed a pices of my bosses ass off. It was then I realized, "When the camera, starts signing the checks, you can make it for what the camera sees. But until then, you have to make it for what the director and actor see."
If you are looking to start with a skill that can work in a variety of disciplines, then, with 3d printers getting so good, and cheap, 3d printing is going to be the way of the future. So if you are going to learn any skill, I would say 3d software and 3d printing will be your best option.
Lastly, Portfolio.
I'm sure everyone has a portfolio in some electronic form these days. (I'm from the printed, in a traditional portfolio age)
Only put in your portfolio what you have made, or contributed a significant amount of work too. Don't take credit for what you didn't do. Don't include pictures of other peoples work. Sounds dumb, I know, but I have had people come in for a job interview and show me their portfolio, only for me to find my work in it. A friend John got a model building job at a very prominent model shop here in LA, even though he was not a "model builder". Surprised he got the job, John asked the owner why he had been hired, over some of the other model builders applying. The owner responded, saying John's portfolio was one of the few he had seen that didn't have something he had built in it.