I like the Topeak Race Rocket mini pumps. Used one for more than a year, several flat repairs. While the HP version isn't ideally suited to my tires, it works fine. The HP is intended for skinny, high pressure road tires. I use wider most-terrain tires at around 40-60 psi, so the MT version would suit me better -- I plan to buy that for my second bike. But the HP version has worked fine -- just requires more pumps to inflate to working pressure. I'd guesstimate about 200 strokes to get my 700x42 Continental Speed Ride back to 45 psi last week after a flat. Not painful to use, despite some minor arthritis.

Lezyne mini pumps look even better for more money. REI carries them locally (I'm in Fort Worth) so you can handle them and see what you like. Fair prices and their membership fee may be worthwhile too.

Whichever you get, be sure it has at least a short extension hose. Much easier to use that a portable pump that attaches directly to the valve. Been there, done that, wouldn't go back to a frame pump that didn't have an extension hose. Threaded attachment is better. More secure, less fiddly, less air pressure loss when attaching/removing.

My basic kit varies:

• The minimum I carry is a Park mini tool (there are several brands and types, all are pretty good, ranging from $15-$30).
• A Lezyne self-sticking patch kit (Park makes a self sticking patch kit too), so no cement needed on the road -- very handy at night, or with cold hands. These are temporary patches -- the Lezynes last up to a month for me. So plan on doing a proper patch with Vulcanizing glue and patches at home later. The Lezyne self sticking patches don't fail suddenly. They just develop a slow leak. Adding air pressure helps seal the leak better so you can still get home safely to finish a proper patch repair.
• A mini pump. I like the Topeak Race Rocket. If I wanted to spend more I'd get a Lezyne mini pump. I prefer a pump I can stick in a pocket when I'm off the bike. Larger pumps are more efficient, though.
• Set of two or three plastic tire levers. Usually I need only two. These are just to get the tire bead off the rim. I can usually get 'em back on the rim with my hands.
• Small first aid kit.
• Small handlebar bag to hold my phone and reading glasses -- it's a lens pouch from an old Lowepro camera waist bag.

For longer rides, farther from home, I'll often carry a few more tools. Maybe a chain tool, spare quick link. Spare tube. Small open face wrench for brake and other adjustments. A more serious first aid kit, usually in a plastic bottle that fits in a water bottle cage. Spare AA and AAA batteries for my lights.