In short, I'd say the car you have. Depending on your city and what you expect from a ride-sharing job, your experience may be great or it may not be. I would not spend money to get into it outside of a vehicle inspection.
If you make money and love it, then consider making it a lifestyle.
A very popular ride-share vehicle is the Toyota Prius. It's roomy, cheap to find used and, most importantly, easy on gas.
All the costs for operating your vehicle come out of your pay, so a low cost of driving is key.
Therefore, miles per gallon is very important in the short term. Reliability is very important in the long term. You don't want all your hard-earned dollars to go to the gas station or mechanic.
Both services have higher pay for rides with more than four passengers. Uber calls it XL and Lyft calls it Plus. Only drivers with larger vehicles can take those rides, giving the mini-van or full-size SUV driver an advantage.
If you drive a bigger vehicle, you can also take solo riders but you'll be giving up money in gas.
Both services offer various benefits for buying or leasing a car, so if you become serious, definitely take advantage.
If you are picking a ride-share car, look at the overall cost of ownership: payment, insurance, fuel and maintenance.
Something sharp will make a good impression on your riders, too, so keep that in mind. And keep it clean, whatever you do.