I would highly, highly recommend going for one of the fun2drive tours. It’s the more expensive option but it’s very well run and incredibly enjoyable. I wanted to drive 2 cars so I did a short comparative drive (30 mins) in an FD RX7 and then the full Ultimate Hakone tour in an NSX. With hindsight I would’ve gone the other way round as the twin turbos and power steering of the RX7 was better suited to the tight and twisty roads, both were brilliant though.
Getting there isn’t difficult, just a bit long. It’s a single bus ride from Shinjuki station, takes two hours but stops literally outside the location. Keep in mind that Omoshiro isn’t particularly close to any train stations. Also Hakone is where you want to be going anyway for that true Initial D experience so that drive out would be the same anyway.
The tour was great, our group was split in to two so I was in the NSX, with an AE86 and R34 GTR. You can ask them to pick up the pace if you feel it’s a little slow but frankly they don’t hang about anyway, know the roads inside out and have more talent than me. The roads are literally straight out of Initial D, they even print out shots from the anime to show you which roads were depicted in the different battles etc. I really don’t think I would have had anywhere near the same experience or driven as hard as that if I just rented a car and went off on my own.
Out of the cars you're looking at I would probably go for the R34 GTR but it's a big car for those roads. The AE86 and R34 in my group were being driven by a couple so they swapped halfway through the day, they seemed to enjoy both cars a lot but preferred the AE86 as you could use a lot more of the power, more of the time.
I was obsessed with getting an RX7 before that trip but it cemented that even further, to the point that I ended up finally buying an FD last year.