First . . . you say "Model 10" - is it marked Mod 10 under the crane? Or does it show Mod 10 - ? (dash something?) indicating it is one of the dash number models indicating changes made as production progressed? Or are you calling an earlier M & P a Model 10? The models weren't marked until 1957. Not that it makes that much difference but if marked Mod10, you can bet it's post 1957. Regardless, you have a good revolver and a good shooter if in good mechanical condition.
As far as 38 spl. as a carry caliber - it's an individual thing. I love the 38 spl. and have no problems at all in using that caliber as a CCW. Some will disagree . . . some won't. For my purposes, it works just fine.
I carry a S & W Model 36 snub. (J frame) which is 5 round cylinder of 38 spl. I also have a Smith Combat Masterpiece 4" - basically like your Model 10 only with adjustable sights and a 1952 M & P with a 5" barrel and a 1920's M & P Target model with a 6" barrel - all fine revolvers. I normally carry the Mod. 36 OTB - and cover with a shirt tail or jacket. I am licensed in two states - both AZ and MI in which "open carry" is legal but I don't like to "advertise".
As far as a 4" Model 10 - it all depends on what you are comfortable with in the way you carry. I don't consider a 4" too long to carry inside the waist but I'm just not comfortable in carrying that way. Either a 4" or a 5" barrel length Model 10 style can be carried in a shoulder holster covered by a jacket fairly easy. I like my J frame Model 36 as it is small but I think that a K frame is just about the "ideal" frame size - at least for me.
I consider the M & P (Model 10) to be one of the finest revolvers made. Sturdy, accurate and dependable. I carry spare cartridges in a drop pouch on the belt. They are fantastic revolvers - I'm an old geezer and was brought up shooting SA revolvers so I am partial to wheel guns. The only time I carry a semi is if we are going to be traveling out in the boonies in southern AZ. Our place there is about 45 miles north of the border and if we were to "break down" - I just feel more comfortable with a higher capacity handgun in that situation as there is a big smuggling problem back and forth across the border - never know what could occur if nobody else was there to help. In that case, I carry a 9mm SR9 with double stack magazines - one in the pistol and 2 spares.
If your revolver is chambered for the 38 S & W Special (38 Special) then that is what you need to use. 357s will not fit in the chambers and don't even try it - too much for the Model 10/M & P. You can use a .38 Colt Short and .38 Colt Long in a pistol chambered for the 38 spl. The 38 Colt short preceded the 38 Colt Long which preceded the 38 Spl. which of course preceded the 357 Magnum. The 38 Colt Short and Long have the same body dimensions as the 38 spl. but their lengths are shorter than the 38 spl. (Think of it like the 22 Short, Long and Long Rifle cartridges - same concept). If you can find any .38 Colt Short or Long on the dealer's shelf (hard to find) they will work in your .38 Spl. which has a .357 (normally) bore size. However, for normal shooting, I'd stick to the standard 38 spl. cartridge - the 38 Colt Short / Long cartridges will probably run more than a box of 38 spls..
I cast my own bullets and reload all of my 38 spls. As such, my experience is primarily with "lead only". I have read many times on different forums that on "vintage" Smiths, you should stick to lead. If you are going to shoot jacketed bullets out of your Model 10, I'd suggest that you have it checked out by a competent gunsmith and follow his suggestions for what you can use in it. I have used FMJ ammo in my Smiths with no problems but stick to lead for my shooting because of the fact I cast my own and reload. In my del 36, I carry with FMJ HP ammo. This model served many LE officers for a number of generations and there was a reason why it was held in high esteem. Again, I am very confident in a 38 spl. - especially at SD range but it is also a "personal thing".
Good luck and I hope you'll post some photos of your revolver. We all love pictures . .. . especially of S & Ws!