Recommendations:
the only firearm authorized is a standard police 38 or 357 caliber revolver with factory 38 caliber ammunition.
Smith & Wesson:
.38 Special Models 10/64, 15/67 with a 4" barrel.
.357 Mag Models 13/65 19/66, 27, 28, 581/681, 586/686 with a 4" barrel
(Slash "/" denotes guns that are twins as blue/stainless model numbers)
For lowest cost, generally the fixed sight Models 10, 13, 64 or 65 will be the best bet. For a fixed budget, a "Heavy Barrel" model 10 or a Model 13 can often be found for $250 to $300. Alternatively, a good Model 15 is a fine adjustable sight revolver in the same price range.
Note that the Models 27 & 28 are huge frames and very heavy. Also that the 58x/68x series is somewhat larger & heavier than the lower model numbers.
Taurus:
If the budget is very tight, take a look at the Taurus Models 65 and 82. These are .38 (M82) or .357 (M65). Their Models 66 & 627 have a 7-shot cylinder. Many holsters that fit S&W "K" frames (.38/.357) will also fit the Taurus guns. Be sure to check the fit yourself however.
Ammunition:
Carry/Duty ammunition should be between 125gr and 158gr bullet weight, ideally a jacketed hollow point (JHP) such as any of the following (in no particular order);
- Winchester Silvertip JHP
- Remington Golden Saber
- Speer Gold Dot
- Federal Hydra-Shok
If these premium bullets are too expensive, look for the so-called "generic" ammo, such as;
- Winchester-USA (USA-38SP)
- Remington-UMC (L38S2)
- PMC ammuntion (38D).
Bullets that are under 150gr usually produce less recoil.
My preference would be Federal's Hydra-Shok 129gr JHP or Winchester 125gr Silvertips.
While the Crimson-Trace laser grips may help (and CT should make grips for most of these guns) you will have to do considerable shooting with your "duty" load to determine the correct offset from the laser at different ranges. For grips that'll cost as much as the gun, I'd shell out for a gunsmith to install a Trijicon night-sight tube in the front sight.
Invest in a good gun-belt & holster with a retention system. This will help prevent someone from snagging your gun in close quarters. My preference (but I'm an old fart) is a thumbreak duty holster. The gun should fit the holster snugly and release smoothly. Many security folks with 4" guns opt for a "high ride" holster, especially for driving or desk work as it keeps the gun tucked in high along your side. I'd avoid "swivel" holsters and low-riding holsters for security/retention reasons.
Additional items would include speed-loaders (Safariland or HKS) and carriers for them. If these are too pricey, see if old-fashioned "dump pouches" are in the bargain bin and buy some Bianchi Speed strips for them. Learn to use them. Mount spare ammo on the front, same side as your holster (strong side).
Invest also in a good flashlight and carrier if you can. Mag-Lites are good but note that the longer "C" cell lights fit nicely into a baton ring! Get at least a 4-cell. A bright Xenon "tactical" light should also be high on the list of items. Usually batteries are pretty pricey, but these lights can also "blind" someone for a few long moments and prevent a serious fight.
Remember your mission is "observe & report" and if necessary, protect life (including your own!). You're one man, usually alone and if you get whacked no one will get your report.