Sounds like an issue with the syncro on your second gear. Read the link below to get a better idea, but basically when you shift gears, the ratio between the input shaft (from the engine) and the output (to the wheels) changes, simular to a bicycle, the speed of the pedals change when shifting gears but not the speed of the wheels and rear gearset. The speed of the output shaft is steady because it is basically attached to the wheels and the speed of the car is not going to change while switching gears, soooo the input shaft speed needs to change to match the new gear ratio that you are switching too, when you step on the clutch, the input shaft is disconnected from the engine, but is still spinning because it is still engaged with the previous gear (1st in your case). When you put it in neutral the input and output shaft are separated, and the input shaft is free to spin at any speed, but it is still not spinning at the correct speed. Once you get it in the next gear, the input shaft speed is slower and hence the reason you hear a different tone from the engine and see a different RPM on the tachometer after releasing the clutch.
Modern transmission have what are called synchronizers which assist in making a smoother transition to the new required input shaft speed. When a syncro starts to go, you will have trouble with that one gear. You can try mastering double clutching which is a technique used for smooth shifting for older transmissions (pre-syncros), which is explained in the first link below. Takes some getting used to, but once you get it, it is like riding a bike (little mustachian pun).
For anyone else reading this, if you are having trouble shifting into all gears, its most likely an issue with the clutch system not fully disengaging, if hydraulic then a bad master or slave cylinder, or a stretched or misadjusted cable on a cable system, or a bend clutch fork (unlikely)
Good luck, and unfortunately sycnro's aren't a DIY replacement job, but getting a junkyard trans is managable with a friend with some mechanical no how and some thank you beers of course.
http://www.howstuffworks.com/manual-transmission-synchronizers.htmhttp://www.howstuffworks.com/transmission.htm