I just want to give a differing opinion here (just so the OP knows that there are differing opinions out there)
People like to use the argument "with all things being equal" when it comes to typing. The problem is - not ALL things will be equal. Everyone is unique (just like you learned in kindergarden). Everyone will have different background - different childhood, experiences, ECs, grades (GPA might be the same but grades in courses might differ). Personalities are different and it shows come interview time. How a person handles high-pressure and stress also differs. So don't worry about the "with all things being equal" aspect (unless you have an identical twin, have the same sets of friends, dated the same people, went to the same school and got the exact same grades in every classes and identical score on MCAT and joined the same club and did the same EC and got the same experiences out of them ,etc - do you see how ridiculous the argument is?)
Now back to the original topic
Type or handwrite? My response: That depends. If the secondary is a form in which you have to fill out, then handwriting is acceptable (as long as it is legible to EVERYONE). Would it look better if you typed it? Probably. Will it have a huge impact? NO (unless of course it is evident that you just didn't show much care for the secondary). In my mind, a neat handwriting also shows professionalism (probably because it is so rare to find neat handwriting nowadays). Just don't do it in rage red, cute pink, neon green, or other "unprofessional" colors (black is preferred over blue because it is easier to photocopy - that's why all hospital records are in black ink)
Now if you were submitting an attached essay (or short responses), typing it on computer and printing it would be advised.
Buying/renting a typewriter for just this purpose seems a bit excessive to me (but if that's what you want to do - go right ahead)
I understand what you guys are going through. You're nervous about making costly and grave mistakes, looking for every advantage, trying to decide the course of your future. But also be aware that admission people are also reasonable and understanding people (for the most part 😉 ). They will look at all aspect of you (qualitative and quantitative). They will make their judgement based on YOU, and not whether you typed or handwrite your quick responses on the secondary, or if you used regular envelops or the 9x12 envelops, or whether you deliver it via USPS, UPS, FedEx, or hand-deliver it accompanied by honor guards and brass band.
For the record - I did handwrite my quick responses and typed/computer-print my essays. None of the schools raised an issue.
P.S. However, if your handwriting is sloppy or looks like you wrote it quickly and without much thought - it will give a bad first impression.