ive only done taking apart gears when i use to go to auto school. my main stregth is driveability issues and no start conditions and engine performance. but sicne you told me that your problem affects second gear as well, then im pretty much sure that you need to change the synch gears for first and second gear.
cost might vary depending on the shop. you will probably get charged like a clutch job rate.
you cant do this at home coz it requires using a press to take apart the gears.
try looking for used tranny at junk yards and weigh your options on wh3re you could save money.
while your at it, might as well put in new clutch