Wow,too very early planning :)
Before main Q you should learn basic info of weather conditions of Japan.
Early summer still rainy season as "tsuyu[梅雨]" not recommend.
After tsuyu super hot summer comming over 30℃ and evening rain with usual.
Don't forget to get enough water or sports drinks before purchasing easy.
Q)How to ride train,bus or ferry with bike(cycle)? (as 輪行"rinko" in JP)
In Japan(Shikoku,too) few cycle train and No bus with cycle carrier/rack.
So need packed bag(or just covers) usual but no need luggage fee plus.
But High(EXP/toll)way bus not accept spl size luggage sometimes
bc bus luggage space not always enough especially booking full or crowded.
Ask before booking at airport bus ticket or general info counter.
Small(short ride) ferry no need packing but need small fee(50-200Y) plus usual.
Q) Which air port better?
FUK or KIX both are not close not good to Onomichi first as dep point.
http://www.ononavi.com/access/detail.html If FUK by bus or train to Oita then by ferry to Yawatahama port cheap.
If KIX by train to Wakayama port then by ferry to Tokushima port
or by Highway bus to Tokushima or Takamatsu stn no transfer fastest.
Anyway open Google map and borh air port web access info pages.