You don't really say what you need/want this gun for so it is hard to really give a good suggestion. I will assume based on this fact and that it will be your first .357 that you are looking for a general purpose revolver.
For the largest variety of missions a mid sized revolver (such as the S&W K-frames) with a 3", 4" or 5" barrel is probably your best option. A K-frame is big enough to comfortably handle most (or all) .357 loads and is strong enough to last quite a while, however should you decided to carry it it is small enough to carry concealed (especially with the 3" or 4" barrel). A 3", 4" or 5" barrel will give you plenty of accuracy and be long enough to get some expansion out of JHP ammo (esp. in the 4" or 5" models). The K-frame or similar model (midsize frame) is much smaller and lighter than the larger framed models (such as the S&W L-frame) so better if you should ever decide to carry yet big enough that it is very comfortable and reasonably strong.
I have a S&W Model 65LS. It has a 3" barrel and fixed sights yet is very accurate. I live in a state that doesn't allow carry so I bought the K-frame so it would be comfortable at the range and give me the full six rounds for home defense (as opposed to the J-frame and other small framed revolvers 5 rounds) but can be easily carried when I move to a CCW state. As a result of my experience with this gun I have no trouble recommending fixed sights, they are simpler (very important if it's your first revolver), they don't lose their zero (important if you'll use this for defense), should you decide to carry they are less likely to snag on clothing, and they can still be quite accurate.
Here is a picture:
you can also see it at this link,
S&W Model 65LS, as for some reason the image often seems to disappear.
The S&W Model 13 is basically the same gun with a blued finish.
If you are looking for a hunting gun I'd suggest the longer barrels and heavier frames (like a 6" or 8" L-frame or even the N-frame) to handle the hotter hunting loads. If you want a small gun for carry (a lightweight snubby) I'd suggest going with a .38 until you have another .357 and are used to the round or buy the K-frame .357 in a 3" barrel- it will do most of what a J-frame snubby will with less recoil and muzzle flip.
Other good guns are the Taurus line (they make great, value priced, revolvers), and Ruger.
Or would a straight .38 be better at the same price?
Depends on what you need. If money is a major consideration a dedicated .38 is a little cheaper (new it will probably be 10-20% less than a comprable .357). Around here the Taurus 82 (in .38) goes for about $290 while a Taurus 65 or 66 (in .357) goes for a little over $300. Some of the best bargains in guns are used .38s that have been traded in by various police departments- you can get a traded S&W Model 10 for under $200 in good mechanical condition (though the finish is often well worn).
A .357 is much more versatile. The .38 is probably the most versatile caliber but the .38 gun can only shoot .38s while the .357 can shoot .357 mag AND .38 spl. However, a dedicated .38 may be a little more accurate when shooting .38s.
My suggestion is to buy a .357 first (take advantage of the versatility of the .357, in effect you have two guns in one) and then later buy the .38.