I saw it today, and yes it did seem odd that ranged weapons weren't used. The Plasma guns on the one arm obviously have some range, when they checked for a "pulse". Sure we see in the opening fight with conventional forces bullets literally bouncing off the Kaiju's scales.
Coyote Tango (the one from the Tokyo dream/memory sequence) used autocannons that looked much like the Shadow Hawk's, one over each shoulder. But long range weapons were phased out as Jaegers were upgraded because simple brute force trauma (punching) left less toxic residue seeping into the environment. Also, Rule of Cool says punching and kicking > shooting. It might be battletech to shoot it with your gauss, but most of the time in giant robot fiction it comes down to physical fighting.
But in the end the thing still died from conventional weapons. Seriously though they couldn't come up with a Jaeger sized rifle or a use of supporting missile fire? And who's bright idea is a wall of life anyway? Or how about once you figure out the timing of when the big old bad monsters come out of the rift, stationing a few ships on the surface and dropping nuclear depth charges?
Nukes ended up having to be used to stop the first few Kaiju. (the movie showed how fighter jets & other conventional units were useless) Jaegers were created to avoid having to keep using nukes, which do even more damage to a city than a giant monster rampaging in it.
As for why not station subs/ships with nukes and blow 'em up as they come out of the rift? Because then we wouldn't have robot vs monster fights. Rule of Cool, man! And I guess because they didn't want to incentivize the Kaiju into evolving ways to come out of the rift stealthy-like.
My main issue would be that the Jaeger production had been cancelled though. Its a weapon system that works, even if the tide is turning against them in a one on one fight, so why not deploy more Jaegers at a time? Each of those bases should have been sending out a dozen for every Kaiju, not one or two.
Plot device man! There's only a few Jaegers left.. every time one goes down it's that much more of a punch because there's no more to fill in!
Plus, committees do plenty of stupid things. It's hardly implausible, especially for a large bureaucracy, to decide that Jaegers are too expensive to continue to develop and produce, only to go instead with an even MORE expensive, unproven option.