I am thinking about making a single-sided through-hole PCB, but using a double sided PCB instead and leave the top side as pretty much a solid plane (minus clearance for holes) and use it as a ground plane. Then I can just make vias for connection to ground.

Will this introduce capacitance into my circuit? I think it would, as now the entire PCB should be a big capacitor (plate>dielectric>plate = trace>pcb>plane).

If I'm right, and doing this turns the PCB into a big capacitor, would that hurt me or help me? Would it help out my decoupling/bypass caps?

 

It really depends on the particular circuit and frequencies involved.
In most cases it helps to keep overall noise levels down.
The capacitance is not large unless you have a large area on the top side.
Continue to use decoupling caps as you would but this time put the ground lead of the cap (if through-hole component) through a hole to the bottom side.
If using SMD caps, use ground traces on the top side which are connected to the bottom ground plane via feed throughs.

If you are going for a solid ground plane consider doing everything in SMD components. This way you do not have to drill too many holes except to connect to the ground plane.

I make SMD prototyping circuits by hand by cutting out channels with a sharp Exacto knife.
You can etch the boards if you wish but you have to think differently. You are literally creating squares and rectangles of copper islands separated by etched out channels.

 

Another thing to keep in mind is that when you try to solder a lead to the large groundplane, you are going to have a really good heat sink that is going to suck the heat away from your iron. Unless you have a pretty high wattage iron, you may not be able to get a good connection. The normal solution is to use pads that have thermal reliefs. Think of a pad that is a donut, then imagine a larger donut around it that is etched away (this is what you might do for connections that do not connect to the groundplace), then imagine a an 'X' or '+' of copper centered on hole with the thickness of the lines about the same thickness as the hole itself and that is big enough to extend into the ground plane. This will give you good enough electrical conductivity to get a low resistance electrical connection (as long as you aren't working at high RF frequencies) but low enough thermal conductivity that you can get a good mechanical solder joint.

 

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If using SMD caps, use ground traces on the top side which are connected to the bottom ground plane via feed throughs.

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Alternately, a good way to connect SMD caps to decouple SMD ICs is with a flooded ground plane on the top (IC side) of the board. Then the cap can be directly connected from the IC power pin to the ground plane with no via in the path to add series resistance and inductance. To minimize the parasitics even further, place the hot side capacitor pad in series with the power trace to the IC. That way the decoupling inductance and resistance between the supply line and ground is essentially equal to the value for the capacitor package itself.