Personally, I print my photos at home (on a very nice, very expensive and somewhat finicky printer), but I am not a typical photo consumer. I am a bit of a control freak when it comes to photos. Sounds like you want a one-click-and-forget-it solution.
Getting an exact match (or even something close) between the image you see on a screen and the same image printed on a piece of paper is a very difficult task, and one that has posed (and continues to pose) a lot of technical challenges. On your screen, an image is made up of light (literally, it's lit up). On a piece of paper, the image you see is created by laying down ink (or ink-like stuff), and the colors you perceive result from light bouncing off that paper and ink, with some wavelengths (colors) being absorbed or reflected, to your eye. Add to that there are some colors that are nearly or completely impossible to reproduce in prints, unless you use fancy/complex (=expensive) technologies (for example, grass-green and oranges are particularly tricky). From a technology standpoint, this is a very, very difficult problem to solve. There are ways to do it, but most are expensive and/or may require human judgement. It's a miracle that cheap "drug store" snapshots turn out as well as they do. If it's any consolation, things have gotten much better with this in recent years. But it's still tricky.
Another problem is the "shape" of your photos. If you simply send your images off to someplace and tell them "just print them", you may have some compromises. It's a competitive business (there are plenty of places that can/will do this) but unless you are willing to pay to have some human actually look at them and -- more importantly -- make (good) decisions (eg: don't cut off the top of a mountain, don't cut off someone's head) you will be at the mercy of the algorithms that were built into whatever system they are running. Photo printing systems are largely automated -- they need to be, to keep the costs down. Consumers demand cheap photos, and are not willing to pay for what it takes to have a skilled, attentive technician make judgement calls and figure out what's best. So you get a headless Matterhorn or family member. Consider how much you paid for those prints. You can take your images to a more upscale place and they will print them however you want (you'll need to be very specific) , but it'll be (a lot) more expensive.
You can probably find some reasonable medium (I'm sure others will chime in) but you will need to keep in mind when shooting your photos that they will be printed by robots. That means you better stick to standard aspect ratios (shapes). Software will allow you to create/edit photos to any dimensions (and modern cameras will allow you to specify all sorts of options for dimensions, some of which will not match the size of the paper they'll print on...that will result in either things being cut off, or large "blank" areas of white).
You need to pay attention to what options you select when shooting your photos, and when editing them (if you do) and when setting up your print requests. Just like when shopping for flights, "be careful what you ask for"...if you just say "I want it cheap" you'll get something like that, but it may not match what you really wanted.
Hope some of that helps a bit.