Good question! This is something that I struggled with the first time I interviewed at a startup as well. But having gone through the process and actually now having interviewed a lot of people as a startup hiring manager, I think I can give you some advice.
First of all, its obviously better to be overdressed than underdressed as a general rule. Also consider your audience (i.e. what position you are interviewing for and where your hiring manager used to work). If you're going for a sales or investor relations position, you might want to dress up more than for a product position for example.
What I would stay away from:
Business professional (i.e. full on suits, fancy ties, cuff links, etc.)
Sport coat and slacks is probably still a little formal, but acceptable
Any intense heels as a woman
What I would wear/have seen people wear:
Slacks/nice jeans with a casual dress shirt
Slacks/nice jeans with a polo
Nice jeans with a sport coat
Stick with the dress shoes (instead of sneakers)
Chunky sweaters or fun/colorful blazers for women
Skirts/slacks/dress with modest heels
The biggest take away I would give though is that an interview has much more to do with a person's personality than what they wear. As long as what you wear isn't completely outlandish, the primary focus should be having a friendly, open and non-"stuffy" attitude.
Hope that helps!
I didn't experience that specific experience directly because I interviewed with a large firm while still in college, but I definitely experienced it in my job transition around the 5 year post-college mark. I was trying to move from a large firm consulting M&A role into a private tech startup Finance role which can be a tough leap. I was able to do it by employing some of the advice that Chris mentioned in his post; I molded my resume and the way I spoke about my previous role in interviews into descriptions and language that the interviewer could understand and tie to success in the new role. It also took perseverance and applying to a lot of positions, and I can guarantee that every single position I applied to had "requirements" above and beyond the experience that I had. Employers expect people to apply even if they don't check the box on every requirement, so definitely do not get discouraged!
I agree with the other comments; in my opinion you should focus on gaining exposure and experience in the type of role that would interest you instead of shooting for whatever random role at a "dream company". Once you have demonstrated skill and competency in the field you like you'll have the background and resume to apply for the type of job you want at the dream company. If you take a random role it might actually spoil your chances of getting the job you want there in the future.
I know some people that have taken contract positions, but it's usually for the exact type of role they would want to be in, and like you said, no guarantee that you'll get an offer and at that point your chances of getting another role at the same company are slim.
I think an important factor is what you want to do exactly (as you said, "Business" is relatively broad). I've seen people with Business degrees go into Finance, Marketing, Operations, Customer Success, Sales, etc. Depending on where you want to go, you can leverage your prior experience to help fit the experience requirements. For example, any type of customer service job cultivates skills that are important in many of these roles. You could also take specific one-off classes (such as if they are requiring knowledge of Excel or SQL or some other software) to fulfill the "experience with" aspect. Keep in mind that jobs descriptions ALWAYS ask for more qualifications than required; it's worth it to apply even if you think you are underqualified. As always, networking is extremely helpful getting a foot in the door - if you have any friends or acquaintances that could help provide an introduction that is usually a big plus. And most importantly, don't let yourself "stagnate". If nothing else, volunteer at an interesting company, attend events, write a blog, or do something else personally fulfilling that will boost your resume while you continue to look for your next role.
In my opinion, no, not at all. Everyone knows a job isn't just about money. If they can't match it but you still want the job because you like the company and the role is exciting, that isn't something that would make you look bad. That happens all the time! At least you tried, and most likely you will get at least a bit more than the original offer.