Too old at 16? I do hope you're joking. You are really never to old and 16 is a perfect age - just get going and have fun!
Starting with an acoustic steel string guitar is a good idea. However, forget the 38" or any other body dimension nonsense. It says very little at all. You can play any size of guitar you want. That said. the 38" size is often used on children's guitars or very cheap (worthless) beginner instruments. And yes, some higher end guitars make smaller size (often called parlor) guitars as well.
What you should be concerned with is the scale length (the length of the vibrating string), the neck bulk, fretboard width, action and string gauge (lighter or heavier).
A shorter scale guitar is easier to play due to the somewhat shorter distance between the fret. A guitar with a slimmer and narrower neck is usually easier to play. Lighter string guages is easier to handle (but also give a little less volume). A lower action and a perfect set-up (well adjusted instrument) is far easier to play.
The size of the box may influence the playability a little, but not nearly as much as the factors mentioned above.
As for bramds, prices etc., I strongly suggest you visit a reputable dealer and take a look at what they've got. If the guitar is perfectly set up, then you can have a fantastic instrument with a solid wooden top for approx. $300 ... if you do your homework and try out many various guitars. The difference can be almost like night and day from one guitar to the next, even between the same make and models.
The higher end guitars are more even in quality. However you would expect to pay premium price for a really nice acoustic guitar.
It's like anything else, you basically get what you pay for.
When you have found a guitar that speaks to you - you or someone else will have to play the guitars - have the store add new strings and set it up for your requirements as a beginner. If they can't or won't do this, then your in the wrong store.