What printer fits MY needs?

I've spent a couple weeks here trying to learn about printers, and feel like I know less than when I started.

If I shoot a family gathering or a church or scout function, I usually pp myself , put on a disc and take them somewhere to get printed, or just leave them on disc.
This is for 10 to 100 pictures.

I would like the ability to print a decent picture here, either 4x6 or 8x10. I can forsee printing one or two pictures a week, maybe none for a month. After my "research" I have just about decided not to buy a printer. Between ink cost and ink drying up if it is not used often, I haven't read about a printer that would work for me.

Yeah, I am out in the sticks, and I hate to jump in the truck and make a trip to town just to print one picture. I know nothing of ink or paper types, just want something better than what my $50 HP F4135 prints on copy paper. A starting point. Maybe I am asking for too much.
Thanks in advance, your comments are welcome.
Finn