One of my favorite things about the later Showa series is when other Riders from earlier entries guest-star in a latter Rider's show, (and sometimes several team-up, AVENGERS style), which makes for exciting crossover episodes and story arcs. That said, there's obviously no chance for this in the original show. And I purposely avoided the first KR and watched all of the others thru Black beforehand because of this. I begrudgingly finally checked out the first series last year... and was thoroughly entertained all the way thru, despite no other riders. It is a long show at 98 episodes (the longest single entry in tokusatsu history maybe?) so you have to commit yourself, as it's a long haul. But it was fascinating to see how multiple concepts for this venerable series got their start. The show was a continuously-evolving work in progress. Hongo Takeshi is far & away my favorite of the two Riders, though Hayato Ichimonji is fun too, and something of a scallywag. LOL. Tobei Tachibana is a great character and it's interesting to see how he slowly evolved into a mainstay supporting character throughout the first five series.
Sorry for the long scrawl.
Short answer: NO, you don't need to see KR to enjoy V3. But it is worth it to check out the whole first series at some point in time. It is rough to get into some of these shows for younger fans, as the effects and breakneck filming schedules make for some cheapy shows, in comparison to the more polished KRs of the Millennium era. Even so, you can definitely see where these later KR shows got their roots as the foundation, while kinda rough, is most certainly a strong one. Perhaps the best thing about Kamen Rider, is that it's such a popular show that nowadays all of the various entries have been fully subtitled by someone or other (with the exception of X-Rider, which is still in-progress), allowing English/non-Japanese speaking fans to finally sample to their heart's delight (and actually be able to understand & follow) any or all of the shows, all the way through. A great time to be a fan! Hope my rambling answer helped you, somewhat.