Raichu isn't as popular as Pikachu, but as its evolution, it is definitely the stronger Pokemon.
Many players go through Pokemon Red and Blue without ever catching a Pikachu. If they do, they often keep it as a Pikachu rather than evolving it into a Raichu. This is due to Ash's Pikachu in the anime.
In Pokemon Yellow, the starter Pikachu cannot be evolved. Any other Pikachu, including those caught in Red and Blue, can be exposed to a Thunder Stone in order to evolve it into the scrappy Electric-type Raichu.
The best moveset for Raichu in Pokemon Red and Blue
Thunderbolt is generally considered a better choice than Thunder. While Thunder does way more in terms of damage, Thunderbolt is very powerful and a sure thing. Thunder doesn't compare in the Accuracy department. It has a decent chance of paralyzing the opposing Pokemon and gets a Same Type Attack Bonus when Raichu uses it.
Thunder Wave is a status move that ensures paralysis. While Thunderbolt has a chance to cause paralysis, Thunder Wave will simply make it happen. It cannot paralyze Ground-type Pokemon, because they are immune to Electric-type attacks. Other than that, Thunder Wave does a good job of slowing down opponents. Raichu is pretty quick and this will give it the first attack with no issue.
Submission is a Fighting-type move that gives Raichu further coverage. A lot of Ground-type Pokemon also have a secondary Rock-typing in Red and Blue. This will give Raichu a move to do supereffective damage against those it is weak against. Submission does do recoil damage though, with 25% of the total damage dealt back to Raichu as well.
Body Slam is yet another attacking move for Raichu in Pokemon Red and Blue. Its base Special stat and Attack stat are even, therefore it can put both types of attack to use. Body Slam does a ton of damage and has a huge chance to paralyze any Pokemon that isn't a Normal-type. It is just another strong attack for Raichu to utilize.