I do tend to print my own photos but there is a lot to consider. Take just the paper you want to print on, there is matt -gloss- semi gloss etc etc let alone makes. That can produce different effects. Then there is the printer itself another minefield to wade through . I prefer to use Epson with Ilford gallerie smooth gloss which is a quick drying paper.
Another point to take into consideration is a monitor shows back lit photos which is a lot different from looking at a hard print. There is also a question of which print ink you find the best for your printer.
I used to use Color munki to match hard copy to monitor but soon got rid of it as that depended on ambient light at the time. A right pain in the backside and having to scan up to 3 times on a colour patch you print out ( just don't even think of it) before you actual print.
having said all that apart from the expense of printer ink and paper there is great satisfaction in seeing the finished hard copy you have produced yourself. To me printing ones own is the end result of photography.
Yes sending away for prints are cheaper and easier definately BUT only you really know the colours that you capture at the time, so can get I believe a more accurate representation.
If a lot wanted printing then certainly send them away, but for individual prints then have a go
One of my own prints and my original photo
this picture of the picture was taken in Jpeg ( reproduction here unedited) and looks even better when seen physically. Chair back used to hold picture upright hence the curve at the top
It takes time but the results are well worth it
Printer Epson XP 950 (now latest version updated to 960) = around £170/200
Ilford gallerie smooth gloss 5x7 per 100 pack = £20/30 Above is larger size,so more expensive
Printer ink Epson multipack 24XL Approx = £80
Just to give some idea. So you really have to be selective which photos you want to print