Q: Warm engine, long starting and feels like it isn't getting gas, 10 sec, then takes off like nothing wrong. Doesn't happen all time

After car is driven and engine warm, shut off for 10 mins or more, the car is turning over a long time before starting but it does start. Switching from 1st to 2nd gear it feels as though it is dying, like it isn't getting any gas and no power at all to go forward. Push in the clutch and rev the engine and there is nothing for about 10 seconds, feels like it isn't getting gas. Then all of a sudden it will "get gas" and takes off like nothing is wrong and may or may not do it again that day. This doesn't happen every time and when I have had my mechanic for a drive, it didn't happen. Never know when it will happen and I don't give it a chance to stall so I am not sure if it would. Seems to be worse when the weather is warm.

My car has 120000 miles.
My car has a manual transmission.