The walks published on this website are quite wide ranging. Some are very straightforward short walks staying on paths whereas others are full day hill walks taking you off path in remote countryside. What you take with you will depend both on the type of walk and the expected weather.
For a short easy walk not to far from civilisation you may need nothing more than suitable footwear. If you will not encounter any refreshment stops on the route, then it would be a good idea to take a few snacks and a bottle of water with you. If your route is not going to be straightforward to follow (most of the walks on this website are not waymarked trails) then you should have a suitable map with you.
A hill walk however is a totally different proposition. In this case you need to be self sufficient to look after yourself for the full duration of the walk. You should also consider the situation that could arise if something goes wrong eg a minor slip causing you to be unable to walk back to your car. For such situations you need to consider whether the equipment you are carrying will enable you to survive out on the hillside (in possibily inclement weather) potentially overnight. For this situation a survival (bivvy) bag, extra warm clothing, additional food and a torch are essential.
A good summer hill walking equipment list is available from Mountaineering Scotland at http://www.mountaineering.scot/activities/hillwalking/getting-started/essential-kit. This list is pretty much the standard kit than every summer hillwalker should be carrying.
In winter when there is snow and/or ice on the ground you will need additional equipment. Please see http://www.mountaineering.scot/activities/mountaineering/winter-mountaineering/getting-started/clothing for information on winter equipment.
Detailed information on what to take with you and wear, along with some hints and tips, can be found at the Mountain Safety UK website.
If you are looking to buy new kit, it is worth doing a bit of research before spending large sums to ensure you get the right kit for the job. The following websites should help you.
Many of the larger outdoor stores also have “buyers guides” on their websites to help you know what to look for when buying kit.