Solar arrays are horrendously inefficient, and not really worth the effort, even if you're in full on easy mode. They're really only useful as reasonably portable end game free energy generators. Geothermal generators, however, and even moreso their cousins the thermal generator and magmatic engine, give you a large amount of power for a relatively small amount of materials, and lava production is very easy to automate. For someone starting out, I can't recommend lava strongly enough as a midgame power source.
As for your quarry, four stirling engines is not going to cut it. Each Stirling engine produces 1 MJ per tick at full speed, while a Quarry can use up to 48 MJ/t. Furthermore, if you're daisy chaining the engines together, as many new players do, the only engine that's actually providing power to the quarry is the one actually touching it. In order to properly power a quarry, you're going to need at least 10 MJ/t. There are a number of ways to do this, but the first thing you're going to want is better engines. Stirling engines are weak and woefully inefficient, and really only have their extremely low cost going for them. Three magmatic engines should keep the quarry going at a pretty decent clip, at 4 MJ/t apiece. Just make sure to connect them to the quarry via conductive pipes or redstone energy conduits, or their power is just going to be wasted. If you want to use the coal coke you're already generating, I'd recommend making five or six Steam Engines (or eight Hobbyist Steam Engines) instead. Steam engines need a steady source of water, so you'll need to make an infinite water source, put an Aqueous Accumulator in the middle of it, and then pipe the water into your engines.
EDIT: Yeah, if this is your first time playing, you should set your sights a little lower. Instead of shooting for the crazy end game UU matter shenanigans, take your time exploring the mods, and try to get a solid understanding of how the buildcraft and industrialcraft energy systems work. I'd focus on Thermal Expansion first, since it's extremely user friendly and can help you get resources together to start exploring the other mods. Thermal Expansion also gives you great tools for setting up an infrastructure - Aqueous Accumulators, Liquiducts, Redstone Energy Conduits, and Redstone Energy Cells.
As for Grydian's recommendation, boilers are extremely powerful ways to generate lots of energy, but they are not something I would recommend to a newbie by any stretch of the imagination. They require huge amounts of resources to make and fuel, a solid infrastructure to actually use all that power, and extensive automation to keep them running. You might want to explore using them down the road a ways, but for now I'd focus on the essentials.
