Here is something that job seekers such as yourself should take into consideration, be it for a part-time, contract, or freelance job.
It is comfortable working in a big company – policies and processes in place, lots of financial and manpower resources, everything structured including your career path, business comes to the company instead of having to chase for business. So if job seekers such as yourself like that kind of environment, you should choose a big company.
However, your work exposure will be more specialized. Example, if you work for an MNC in finance, you may do only Accounts Payable instead of a full set of accounts. So this path may not lead you to becoming a CFO in the future.
If you thrive on challenges and in a less structured environment, a small company is better. Resources are always stretched, businesses must be chased. So you will learn more, grow faster. If you are a performer, you will stand out easily. But a struggling company is not ideal if you are always fighting to stay alive.
You can start out in a small company for the learning. Then after you earn your stripes (and promotion), apply to join a big company, confident that you can handle more challenges. But remember, it all depends on your character and what you want.
Ultimately, whether it’s a big or small company, or if it's a full-time or part-time/contract/freelance job, how well you do depends on your attitude.