Hexagonal and Torx allen keys are the two most commonly used tools in tightening various parts of the bicycle for instance, the handlebar, stem, steerer tube, seatpost, saddle clamp, bottle cages.
You can purchase these allen keys from any hardware shops or bicycle shops. The allen keys comes in two types of packaging. In my Torx key set, you can see that it is portable to be stored in a saddle bag. In my Hexagonal key set, you can see that it is not portable and meant to be kept in storage box. Hence, you must decide where you plan to keep it and get the appropriate packaging.
Hexagonal Allen Key comes in 1.5mm, 2mm, 2.5mm, 3mm, 4mm, 5mm, 6mm, 8mm, 10mm. The common sizes used are 4mm, 5mm and 8mm. Seatpost, Stem, Steerer Tube varies between 4mm or 5mm depending on brands. As 8mm are used to tighten the most pedals onto the crank arm. You can either use the 8mm allen keys from the set or purchase an individual 8mm pedal wrench as shown in the photo below. I would strongly recommend getting the pedal wrench to be used at home. The reason is the additional leverage due to its increase in length. In order to help you understand this concept of using a pedal wrench, I will use what we learnt in physics to illustrate this.
Work Done = Force X Distance.
Hence, with the same amount of Work Done and longer length of the pedal wrench, you literally use lesser force to tighten the pedals.
Torx Allen Key comes in T9, T10, T15, T20, T25, T27, T30 and T40 according to my above photo. The commonly used are T10, T25 and T30. Stems from 3T uses T25 nuts (newer models)
For more precise tightening the nuts on carbon materials, it is recommended to use a torque wrench to do achieve the job. I am using the Lezyne Torque Drive Wrench. The main reason I chose this model is because its value for money compared to the other brands offered in the market. It comes in a mini rectangular casing, simple to use and the provided tool bits are Hexagonal 2mm, 2.5mm, 3mm, 4mm, 5mm, 6mm, Torx T10, T25, T30. It comes complete with Flat Head and Phillips Head. If your budget is not a concern, I will recommend you the Park Tools Torque Wrench, available in both analog and digital format. However, it is bulky and not wise to bring for overseas cycling trips.