Apart from the obvious - a bogie - there are a number of safety items I would recommend investing in.
A decent helmet - AKA skid lid, brain bin etc. Full face is going to provide the best protection and is reallly the only way to go. You won't need to spend mega money, especially if you check out the the motorbike shops clearance sections. Modern helmets tend to be lighter and stronger due to constant development and come in a wide variety of shell materials, from polycarbonates, fibreglass, kevlar to carbon fibre. Bicycle, skateboard, horse riding and your grandad's old leather bowl helmet are deffo not going to cut it, though!
As a guide, the following is an extract from the Cairngorm Soapbox Extreme rules.
"The helmet must at least comply with, and carry the appropriate markings for, any one of;
A sturdy pair of boots - these will protect the ankles from knocks especially in the close confines of a bogie. Walking or hiking boots, work boots etc are all suitable. Flip flops, sandals etc are not cool! If racing in open carts, gravity bikes or gravity sidecars, the advice is usually motorcycle boots.
Gloves - depending upon the type of racing, if racing in an enclosed bogie, these will just be to provide some comfort and grip. Try not to wear gloves which are loose fitting as they will just be uncomfortable, ski type gloves, gardening gloves with the sticky pads, leather driving gloves etc have been used, to good effect. If racing in open carts, gravity bikes or gravity sidecars, the advise is usually motorbike gloves. Don't bother asking your mum to knit you a pair, go and buy some!
Body wear - No exposed skin - it comes off, if you come into contact with something rough! If racing in an enclosed racer, a sturdy pair of overalls on top of your clothing will provide suitable protection. If racing in open carts, gravity bikes or gravity sidecars, the advice is full motorcycle leathers and if you have it body armour (not the stuff used in the dark ages)- if you come off, crash, etc these will give you the best protection. No! gimp suits wont do!
Restraints - Usually a requirement for enclosed bogies, but not at all events is a seatbelt. 4 point racing harnesses are not that expensive if you search the web, well worth it. Not only will they keep you strapped in in the event of an accident, but can be a benefit when racing - stops the body from moving / sliding about. Car fixed seatbelts have been used, but don't use inertia reel type, they can be a pain to set up. If using a car seat belt, only take it from a car you know the history of. In the event of an accident the seatbelt weave will give, but only once. After this its gubbed and the next time you have an accident its going to be sore!
BUT, a seatbelt is only as good as the mounting points and position. Make sure these are in the right place and upto the job!
I have seen some events specify wrist restraints in enclosed or semi-enclosed oufits, a good idea to stop the arms flailing about if the worst happens and you get upside down. Just make sure that you don't make them too short or you might not get them undone, until help arrives (or your mates leave you strapped in all night).
Neck protection - it does't need to be a HANS setup to be effective. A simple neck brace will minimise whiplash, but still allow good rotational movement of the head.
OK the above items can add to the cost of taking part, but once invested can be used for many years. Ultimately, if you are unfortunate to have an accident, it will mean you will minimise the risk of serious injury.
Don't let the above put you off, this is a fairly safe sport, with very few incidents resulting in nothing more than the odd bruise and dented ego. Just use some common sense and check out the rules and guidelines of any event you are interested in participating and don't get upset at organisers - they just want everyone to go home safe and not have to fill in H&S paperwork.