I just defeated the Fuchsia City gym leader and am wanting to continue, it says I require a bike, also I would like to know where I obtain Surf HM, anyways bike is more important. I need help, thank you!

You get the bike by giving the voucher in cerulean. Beforehand you obtain the voucher by paying the rent of a npc in Vermillion city.

 

Surf HM is in safari.

The voucher cost 75,000$

And HM Surf is much more important than bikes :)

As others said, you get a bike voucher from the guy at Vermillion, but if you don't wanna pay / don't have 75k for it, you can always take the Route 12/13/14/15 way (going south from Lavender town) to get to Fuchsia.

 

You can get HM Surf in the Safari Zone, gotta battle a guy who has a Pikachu in Route 19 first.

148966 I just defeated the Fuchsia City gym leader and am wanting to continue, it says I require a bike, also I would like to know where I obtain Surf HM, anyways bike is more important. I need help, thank you!

 

First of all, you don't need the bike to continue. The path west of Fuchsia is a shortcut which takes you to Celadon City, but it is not required to progress in the storyline. You can always backtrack to Lavender City. You WILL need to go back to Celadon, visit the Celadon Department Store Roof, and buy a lemonade so you can access the next city: Saffron City. Use your in-game map to see where this is located in case you're unsure.

 

As other players mentioned, you're able to buy the Bike Voucher for paying Samuel's rent (75k) in Vermilion City.

 

Surf is located inside a House in Safari Area 3 (inside the safari zone) but you can't go into the Safari Zone until after you defeat Victor on the beach south of Fuchsia.

 

Good luck.