Ideally, I'd like to find a balance between affordability and potential for appreciation.Also, are there any common pitfalls or things to watch out for when buying a multi-family property in Jersey City?

The new pref equity is given priority to the original pref and/or common equity.

Avoid common pitfalls like underestimating costs or tenant management challenges by planning conservatively and staying proactive.

@Jason Sung Yes, this is common.

What are the potential pitfalls and benefits of each approach?

Is it common to purchase a home with other debt?

Whereas if you and the other investors held ownership as TICs (Tenants in common) then you could sell your portion and do a 1031 of your portion while others did something else. 

Is it common for developers to use subsidies to cover 100% of the construction costs without needing to obtaining debt or raising equity?

Do you think it's common for a tenant to sue for an amount greater than insurance can cover, then take your property or even your personal assets? 

I implore you to do one of two things...1) find a partner that's been there, done that, and bought the tee-shirt so you can learn the ropes with someone who knows the pitfalls or, 2) start with a single-family or duplex with the guidance of someone that knows what they are doing.