The quarter wave groundplane should work very well, with a minimum of trouble. It will have the same gain as a dipole, but should have a very consistent omni-directional pattern if mounted with nothing around it.
If you are in an area with repeaters within a few miles, even up to about 15 or 20 miles, a quarterwave groundplane will work just fine with an HT at around 5 watts. Farther if you have a higher power rig and good line of sight, not as far if you are surrounded by buildings.
Anytime you are homebrewing an antenna, the impedance is going to be an important consideration. Any change, even leaving your radials at a 90° angle rather than a 45° droop, can change the impedance and reduce efficiency.
Homebrewing VHF antennas is a great place to start--they are small, easy to handle, and usually quite cheap. The best way to start out is to use the plans and directions you can find on the internet. Start with simple antennas, and then you can move up to more complex types and experimenting.
You might also look at a simple J-pole design, like this one:
http://www.qsl.net/n6bg/thunt/jpole.html
They are basically a half-wave end-fed antenna, and are also simple to make. The performance of a basic dipole is about the same as a quarter-wave groundplane. There is a variation that adds a second half-wave element above the "J" that doubles the gain while keeping an omni-directional patter.
Also, remember that there is great value in getting an antenna up above the ground clutter. Holding a groundplane in your hand is much better than a rubber-ducky, but putting it a few feet above the highest point of your roof will help get the best performance from any V/UHF antenna.
Dave_W6DPS