Hitchhiking in an infinite universe leaves you open only to the options available where you are. If you are on Terra and need to get to Tyrol, and the only ships going to Tyrol are in Nul, you have to hitch to Nul to get to Tyrol. Not great. Hitchhiking can get you in a general direction but not exactly to your destination.
thumbing
Freelancer pulls up
Pilot: "Where are you going to, mate?"
You: "Aiming for GrimHex in Stanton System"
Pilot: "Mmmm, From Kilian? Stantons out of my way, I'm off to Taranis so I can drop you off there and you can try to hitch to Terra and from there to Stanton but traffic is low in Taranis due to all the death awaiting you there, or I can drop you at the next system which is Ellis but you will then nee to grab a ride to Stanton from there or to Magnus and then Magnus to Stanton."
You: "Uh... Ellis?"
Pilot: "No problem, jump in the back. Watch out for the yellow boxes, it's medical waste, used Med-pens so don't let 'em stab ya or you'll be needing one yourself."
Hitching may get you system to system easily but the further out you get the more stops and new rides you'll have to grab to get you places.
For cheap QD equipped ship look no further than the Aurora ES. At $20 there is nothing more affordable, however I'm not sure if they have guarenteed a Jump Drive for all ships yet. The Aurora LX (Dat seat tho) has a jump drive as standard equipment so that may be the best bet.
For something a little more capable I'd say the Avenger base model, again not sure about Jump Drive, but it just seems to have everything you need.
Not sure if there will be Taxi Missions for Players (beware of trolls), NPC Taxis or even rentable ships in the PU like rental cars that will charge for the amount of time you are flying it. Little too early to say.