Freshman Small Consulting Internship - Good for recruiting?

Hi guys, this forum has been amazing so far as a resource to learn more about finance. I'm currently at a semi/non-target doing a search fund winter internship and starting to consider options for this summer (2021). I have a couple of questions that I hope some of the more senior monkeys will be able to give advice/insights on:

1) My current search fund is a recently raised fund (so majority of the work is sourcing/lead generation). Does this mean that there is not a lot of value in including it on my resume? How should I spin it during future IB interviews when they ask me to explain my work experience?

2) I reached out to a couple of small no-name management consulting firms that are local to my town, and got a few interviews. I was just wondering if having a no-name management consulting firm summer internship would harm my chances of breaking into IB as an upper year (I've heard that a common interview question is "if you're interested in management consulting, why recruit for IB?")

3) Would looking for other search funds to intern for/applying for business analyst roles at larger companies be better on my resume? What sort of internships would best position me to secure strong IB interviews in second year for third year positions (given the hyper accelerated recruiting timelines)? Any advice would be greatly appreciated!! Thanks so much.