Time to consider buying the HELM manual (helminc.com) for your car. I agree that the current engine should be fine once the needed work is done. You are describing either rings or stem seals. The seals in the head are not hard to do. The rings will require that the engine either be removed or that the tech simply pull the head and pan and do it that way-if there is enough room under the car. Pulling the cylinder head is going to take time, but is not difficult.

BEFORE you start get a Compression test and Leakdown test done. These should not cost more than $100 and will tell you what cylinders are not in spec. Honda engines DO last for a considerable amount of time and miles with proper care. My CRX has 176K on the Odometer and we think the engine is original. Whatever you decide, make sure to replace the Timing Belt, Water Pump and other accessory belts. THis is very important to do. You may even want to replace all of the hoses if they are original to the car. These things will add to the total expense, but are necessary in the end.

Cleaning the internals of the engine, as suggested, may make the problem worse-get the Compression and Leakdown done first.

Good luck with the diagnosis.