Be sure to reject the worst offenders with a 'flunked the physical' or 'got assigned straight to SWAT, nice NPC, please start again' if you need to drive the point home.
Haha. Nicely said.

To be honest, considering everything the Lone Star officer would need in the way of skills to do his job properly, and what he'd need in the way of gear other than what you're giving to survive those he's supposed to apprehend, it would be wiser by far to give your players a full 500 at least.
I would agree if I were expecting the 4 of them to apprehend 5 person shadowrunner teams hiding out deep in Cutter territory. For the most part, they'll be trying to solve crimes, not stop gang wars. Sure, they'll be in dangerous situations (following up leads at gang haunts, apprehending 1 or 2 dangerous NPCs on the lam, dealing with a sudden attack from a single summoned spirit), but they won't be asked to infiltrate MCT, hack the system, take out magical surveillance, take down the heavily armed corpsec, and steal the paydata. That said, I am reconsidering boosting up the build point total (thus the poll at the top and general question on this point), but I won't be starting over 400 for this game.
The PCs should be special, a cut or twenty above the others in the same profession.
I want them to get to this point, yes. To start with, I want some NPC detectives to look down their noses at some of the fresh meat, some other officers to really get under the PCs skins so that when they break a big case they can rub it in their rivals' faces. (I do also plan to give them some straight allies on the force as well, especially as time goes on).
Also, they likely would have to pay for any implants themselves.
Actually, from reading the Lone Star book, it sounds like officers often end up with second hand cyberware (pulled from various apprehended perps) that was "supposed" to get destroyed. Sometimes if officers go under the knife after a particularly bad run-in with some criminal types, they may wake up with 'ware they weren't expecting and may not even want (thanks to the fine print in their contracts). Sort of a robocop situation but not quite so extreme.
I'd let them, and strongly encourage them, to spend 200 BP on attributes
That is definitely my plan now that it's been brought up.

The Runners Companion p.23 has useful things to say on the topic of public surveillance which suggests they should only provide intermittent leads to the cops. These systems face 3 critical obstacles:
Ooh, thanks for the tip. I will check that out after work tonight or tomorrow. Those obstacles seem very reasonable to me -- should provide some interesting challenges.
I would prefer having the full 400 BP but with some guidelines about how it can be spent. For example, you could require that the players spend 50 BP on contacts and knowledge skills. These are often neglected in a regular game but would especially helpful for detectives trying to solve a case. You could cap active skills at rating 3 ("Professional", by the book's description) to encourage skill diversification.
Mmm...I like that first idea especially, forcing them to branch out a bit. Also, for any of them who may have built their characters at 300 before I decide to boost it, that would give an easy way to upgrade without drastically changing the character. I probably won't cap skill level more than normal though. If they want to be really good at a thing or two, I don't want to hold them back on that.
A fun part of Lone Star work could be allowing the players to have access to really big guns...but they not only have to file reports detailing WHY they need the big guns, but an after-run report as to how the weapons were used, did they prove necessary, etc.
Totally. I don't expect this to be the norm, but I love the idea of them having to gear up extra hard to extract a suspect from a gang-infested, ghoul-ridden portion of the Puyallup Barrens and they can't just bring SWAT with them because of departmental politics. And if it's a big ticket case, their Lieutenant might speed through the paperwork to get them the biggest guns available.
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As for the legality of SMGs and such. It seems pretty clear to me that most of those in the 4th ed core book are just Restricted. Being the people they are, they should have no difficulty getting those guns and holding legit licenses for them. Some Forbidden items will also be available via Lone Star (on a requisition basis only). This makes sense to me since both of the Sniper Rifles in the book are rated F. So the PCs wouldn't be able to (legally) own one, but they could requisition one for specific use. Granted, they probably wouldn't. They'd probably just call in SWAT backup for that kind of thing.
Thanks again for all the advice and feedback so far.