Got hit by a car today

You've been injured. If you really want to do this quickly and simply then at least include details of your injuries (even minor ones). They will either offer you something as a compensatory measure or decide that your injuries aren't worth paying out. That's up to them and if you're happy with that then so be it.

I'm not one to advocate sprurious claims and litigation. However, having been injured, this will have an impact on your life, even if only transitory and it is not unreasonable to expect to be compensated for this. If the company do make an offer that you think is acceptable then by all means take this.

On the subject of legal representation. On one hand they aren't strictly necessary. On the other they can be useful. Firstly, an insurance company will take a claim involving representation a bit more seriously as long as the claim isn't spurious in the first place. Secondly, without legal representation, the company will probably make an offer "without prejudice". This means that once the money is in your account, you can't take the matter any further. If at somepoint after the settlement you discover that your injuries run deeper and have a longer and more significant impact on your quality of life such as a limited working capacity or swifter decline in health with old age. Avoiding that without prejudice clause and getting a claim to pass can be very hard without legal representation. Consider this carefully.

+1

If she's paying you cash for your injuries then you won't need a solicitor. As long as you're happy with the amount she's willing to pay, fine.
If they're going down the route of insurance claim, get a solicitor, because those cunts are going to call you all the liars under the sun and make out it was your fault.
If they call you a liar, be ready for a long drawn out battle, but it will be a battle you'll win. Be patient, and don't settle for compromise.
Claim maximum physical damage.
Claim maximum emotional damage.
Claim for everything on you bike, including rim tape, tubes, grease on the chain, air in the tyres.

You'll need photos of damage.
Photos of site.
Photos of injuries.
Photos of the offending vehicle, if possible.
Witnesses.

Good luck buddy, and start perusing frame builders or bike catalogues, dreaming of that new ride.