Meh. CH4, H2 and RP1 are all clean, cheap fuels - the levels of pollution and fuel costs are practically non-issues here. ISP, thrust and density are what matter. Methane simply lies on the curve between RP-1 and H2 in terms of thrust, density and ISP.
Mostly right. Two out of three for clean: RP-1 has a tendency to coke up and can foul injectors or lead to hot-spots in the cooling tubes if you're re-using the engines. (Merlin's pintle injectors are probably not as prone to coke fouling, and all of this is going to depend on dozens of specific design decisions in the engine.) (The cleanliness of the exhaust is, as you also implied, irrelevant. Expecially compared to storable and/or hypergolic fuels.)
Isp is what matters above a certain altitude, below that what matters it thrust. All the Isp in the world won't help you get off the ground if your thrust to weight ratio is less than one. We've tested nuclear rockets with Isps in the 900s (three times better than LOX-H2) but they were too heavy to get off the ground. (Ion engines have the same problem in spades, but we're not talking about those.) Methane (and RP-1) will give you higher thrust than a comparable LH2 engine. Again, there are tradeoffs -- you could run LH2/LO2 engines O2-rich for higher thrust during part of the launch (although superheated O2 isn't the most benign environment for your pad, or the engine nozzles.)
Glad you brought up density. Many people forget about how this affects rocket performance. For any given mass of fuel (or oxidizer), the denser it is the smaller you can make the fuel tanks. The smaller the tanks, the less dead-weight you're lifting. I believe the latest Falcon-9 super-cools the LOX (making it denser) to take advantage of this. Methane also allows for considerably smaller tanks than LH2, making up some of the Isp disadvantage (the reduced insulation needs and simplified handling also help). (Some of Gary Hudson's old Phoenix SSTO proposals considered using densified (slush) hydrogen to get tankage weight down, but we still have hardly any experience with that stuff, and it's still barely 1/5 density of LCH4).