If you can, I recommend flying the plane home yourself. The first flight in a plane all your own is unforgettable. The only fiddly bit is that the plane might be far away, and since you haven’t taken possession you’re in a bit of a chicken-and-egg situation. How you handle it depends on how for the plane is:

• If it’s close, you can probably get a friend or family member to give you a lift. Remember that you’re now in a very strong bargaining position, since you can trade plane flights for car rides.
• If the plane is based at a commercial airport, you can fly there commercial and hop over to the GA terminal to collect it.
• If you can’t get a ride or a commercial flight, consider a one-way car rental. These are very cheap; usually less than $100/day plus gas. Remember to use your AOPA discount.
• You could get a ride to the plane from a friendly flight instructor. Note that this can get expensive since you’ll need to pay round-trip CFI + plane rental fees.
• If the logistics just don’t work out, you can always get a ferry pilot. This is also pricy; you’ll need to pay all expenses, travel to the pickup and from the dropoff airports, plus a few hundred dollars a day.

Note than on your first flight in the new plane, you will discover a problem that was somehow missed in the prebuy, logbook review, test flight, and final walkaround. No matter how minor, your first instinct will probably be to kick yourself (or maybe the A&P who did the prebuy). Refrain from doing so! Things large and small break on planes all the time; in the long run it doesn’t matter if it happens 10 minutes or 10 months after you bought the plane. This is why you carefully calculated the maintenance costs you expect and developed a good relationship with a mechanic you trust. Keeping the plane repaired is just as much a part of plane ownership as showing it off on the ramp or setting off on amazing trips. Don’t let an early taste of this sour your first flight.