The type of tackle box you use is entirely a matter of personal preference. The fishing basket is still popular and is used as a seat as well as a tackle carrier. The disadvantages of baskets are that they are heavy, and riverbanks are not always conveniently fiat enough for them to be used as a scat. A large rucksack will hold most of your tackle and you can carry a lightweight chair to sit on. For long fishing sessions the back rest on a fold-up chair makes for more comfortable fishing.
All sorts of containers can be used for storing the smaller items of tackle such as hooks and floats. Hooks kept in small tins will be blunted from being rattled around and are best kept in a lined hook wallet.
A strong rod holdall is handy for transporting rods and protecting them from damage.
Although not essential, a large fishing umbrella is a good investment. The umbrella is as useful for blocking off a cold wind as it is for keeping you dry. In very windy weather the umbrella should be staked clown with guy ropes otherwise you could find it taking off. Fishing in winter without an umbrella can be a pretty miserable experience.
A small but handy item of tackle is a disgorger. For the small hook sizes a narrow disgorger with a hollow conical end is the best type. Avoid the types with a forked prong at the end. For larger hooks, and for dealing with sharp toothed fish such as pike, you will need a pair of artery forceps.
Once you have acquired the basic tackle necessary for float fishing, the rest can be accumulated over the years.