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RG6 coax can lose up to about 7 dB (worst case) for every 100 feet. Actual loss varies with frequency, so lower channels (i.e., VHF) might only lose about 3 dB per 100 feet.
RG59 coax can lose up to about 11 dB (worst case) for every 100 feet.
A 2-way splitter will have about 4 dB of loss. Splitters are also known as power dividers since each output gets an equal share of the input power. When a signal is split two ways, each output port gets 1/2 of the input power. Half power means a loss of 3 dB, but since these components are never 100% efficient, in reality you get somewhere between 3.5 to 4 dB of loss.
A 4-way splitter will have about 7 dB of loss.
An 8-way splitter will have about 10 dB of loss.
The Noise Figure on most consumer-grade TV tuners is roughly 6 dB, although some have been known to be worse (like ~10 dB).
Just follow the chain between the amp and your TV to add up how much loss you are going to have. For example, if you have 4 dB of loss from coax, 4 dB from a splitter, and 6 dB due to your tuner's Noise Figure, you have a total of 14 dB of anticipated loss. Since this is a little more than your amp's 12 dB boost, you might actually be losing approximately 2 dB of net SNR due to insufficient amp gain.
Since you already have the HDP-269, I wouldn't worry about these 2 dB. At the moment, I think you're just feeding 1 TV, so you don't have the 4 dB splitter loss. Even if you decide to add the splitter later, I don't think you'll notice the 2 dB SNR loss, so there's probably no justification to go out and spend money if you don't have to.
I'm guessing that you went with the HDP-269 because you are trying to avoid amp overload on some very strong input signals. The low gain (12 dB) of this amp is one of the reasons it is able to handle higher input levels than most other pre-amps.
For people who have very high losses (e.g., very long cables, 8-way splits, etc.), then there's good justification for getting a higher gain pre-amp or adding a mid-stream distribution amp.
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