Solenoid sticking ,tapping to start car?

You can change just the solenoid if the parts store sells it. Otherwise go to a starter rebuilder and buy a solenoid. I've been a mechanic for a long time. I would take the starter off the engine. Then remove the solenoid from the starter. Be careful the big spring doesn't hit you in the face. Then open the solenoid. The copper contacts are probably pitted. I'd file them clean. Most solenoids can be opened, but some can't. It's more than likely the copper contacts, which is just a high current switch.

It is in a a hard to get to spot, so I think I'll take it to garage to have it replaced, but will ask them not to replace it with a cheap one that won't last. I have had this car for 16 years and don't remember ever having the starter/solenoid replaced, even though it had 2 alternators replaced and a few other things over time.

My guess is that the starter solenoid is not the problem, but the starter itself is. It is very common for the brushes inside the starter motor to be worn down and are barely making contact with the commuter. Just like if you have ever looked into an electric drill motor while it is running, in those little vent slots, you see the sparking of the brushes as they feed electricity to the rapidly rotating armature. Those carbon brushes eventually wear down and on your starter they may just barely be making contact. When you hit it it jars it enough to make better contact and start rotating. Some spots on the commuter are worse than others, so like a roulette wheel, it depends on where it stops as to whether it will start next time or will need another knock to get it going.

Years ago I owned a 1991 Geo Prism. That model year sure ran smooth! Very excellent suspension. But replacing the starter was really hard because it was in a very cramped and hard to get to place. It took an hour of struggling to get at it and get it out, and it always left me with sore muscles and a sore back. But it's doable if you have some mechanical skill but not recommended for a complete novice. You only need to remove two bolts and disconnect the wires, but the problem is that it's a struggle to get to reach it to do that.

My problem was that I always replaced the starter with one of those cheap $80 rebuilds which were guaranteed for life. But they never lasted more than 9 months, and although they always gave me another exchange unit, I still had to go through all of that work to remove and replace the starter. It was torture. I ended up doing it 3 or 4 times every 9 months or so, and it was always the same failure - the brushes wearing down and having to hit the starter to get it to start.

Now I don't know if the rebuilds are any better nowadays, maybe the rebuild manufacturer got tired of replacing all of those starters all the time and got their act together. But it's something to consider when comparing the price of a rebuilt starter verses a new one.