you really have 3 options:

1) Quick rebuild. MOst likely your oil control rings are bad, USUALLY you can rering it an be fine. ive done it a few times and had great success. this is doing the work IN THE CAR ie NOT PULLING THE MOTOR.
DOING IT YOURSELF:
Rings OEM HONDA $100
ACL ROD BEARINGS(might as well replace these) $60
OEM HONDA headgasket $65
oil pan gasket $15

MAINSTREAM PRICES
Rings OEM HONDA $100
ACL ROD BEARINGS(might as well replace these) $60
OEM HONDA headgasket $65
oil pan gasket $15
Labor $700

2) A complete rebuild, with upgrades is next in the food chain. you can rebuild with OEM aftermarket parts like pistons, machine work, etc.
DOING THE WORK YOURSELF
Rings OEM HONDA $100
ACL ROD BEARINGS(might as well replace these) $60
OEM HONDA headgasket $65
oil pan gasket $15
Machine work $350 (bore , hone, balance, chamfer)*prices vary*
Lower gasket kit $55
Timing belt and water pump $150
Oil Pump $100
PR3 b16 Pistons $150 (raise compression)
or
CTR PIstons $165 (raise compression)

MAINSTREAM PRICING
Rings OEM HONDA $100
ACL ROD BEARINGS(might as well replace these) $60
OEM HONDA headgasket $65
oil pan gasket $15
Machine work $350 (bore , hone, balance, chamfer)*prices vary*
Lower gasket kit $55
Timing belt and water pump $150
Oil Pump $100
PR3 b16 Pistons $150 (raise compression)
or
CTR PIstons $165 (raise compression)
Labor RR ENGINE $700
Assemble Longblock $550

3) Swapping in a different motor can be a good option as well. in your particular choise you have a few options like a b20, or a b16.
DOING THE WORK YOURSELF
Hmotorsonline.com B20 Longblock $649 +225 shipping
youll ahve to swap your LS intake manifold onto the B20 longblock

MAINSTREAM PRICING
Hmotorsonline.com B20 Longblock $649 +225 shipping
Labor RR ENGINE $700
Fluids $50


Option 1 is the cheapest if you do it yourself, however, on a high mileage motor, the chance is 50/50 it will work. If the bore is out of round, or there is no hone left, then reringing it will work temporarily, but it wont last forever. if there is a factory hone left, then it will 99% fix all your problems. you CANNOT HONE A MOTOR IN THE car with factory pistons. you will have to much piston to wall clearance and the smoking will get worse.

Option 2 is an all out rebuild with machine work which will ensure ring seat, ZERO MILES on the motor with all new OEM parts and you can upgrade to better pistons, and its much more costly, but thats the way to ensure it will work.

Option 3 is a great choice because the b20 offers slightly more TQ, and you can SELL your old LS LONGBLOCK for a few hundred dollars to make some money back.

most people that come through here do option 3. in the end it hurts them less in the wallet and its also a pretty much guaranteed fix as long as you purchase the motor from a REPUTABLE COMPANY like hmotorsonline.com.