I applied for internship in several companies by the start of the month. I had a tricky deadline in another thing so by the end of the month I need to have definitive answers for internships.
I was first answered by one company (big corporation) and they interviewed me twice. They asked me more in the beginning if there were another companies that were in contact with me, to which I truthfully replied no, since no companies had yet contacted me (I made it very clear to them that I had applied for other jobs, but also that they were the first to answer). In the final interview they were still the only company that had spoke with me, so when they asked for the second time I again said they were the only company that I was in contact with.
Now, right after my last interview, another company (small Start up) called me and scheduled an interview for the next day, where they presented an internship offer that was really interesting. We didn't spoke salary nor working hours so I still cannot say which internship I prefer since these two topics will obviously be taken into consideration.
Today, I have received an e-mail from the first company (big corporation) saying that they were happy to tell me I was approved for the internship, and told me to write back whether or not I wanted it. I obviously want to do an internship this year so this might be my only chance, however I would like to wait for the other company's answer (which might take until the actual end of the month) just to see which one I would like best.
Now, I don't know how exactly I should proceed. I see only two options, and I am desperatedly looking for something beter:
1st: I ghost the big corporation for a bit. That is, I keep them without an answer until the other company answers me. This option has the terrifying possiblity of suddenly receiving a mail saying "Since we didn't hear from you, we decided to end the offer for internship". Which would be sad because I liked this internship as well.
2nd: I tell the big corporation that I would like to wait another company's answer before answering them. That would be sort of strange, since during the process they asked me whether or not there were companies speaking to me and I said no, and will also give the (wrong) message that I don't want to do an internship there unless there is no other option. I do want to work there, but if the Start up offers me similar/better remuneration and working hours, I guess I would decide in favor of it, since it's closer to where I live and is very intersting proposal.
What is the most professional way to proceed in this case? I am (really) open to options other than the two described above.