Considering it sort of a plumbing project... also, if possible, keep it as cost-effective as possible? Is there a particular fitting I need to use? And I want the tube to connect internally (tube is inside fitting) as opposed to externally.Thanks in advance!
If it's flexible tubing, there are nylon barbed fittings at nearly any hardware store that will fit your specifications. One end will fit inside the tube, secure with a tightened hose clamp after screwing the threaded end into the female fitting. If it's a pressurized application, wrap the threaded end with teflon tape before tightening. You may have to use a series of bushings to step up the threaded end if the sizes are too far off. Most home stores can fix you right up, must make sure you take all your diameters of the fittings and tube with you.
You would be looking for a Compression fitting that is suited for plastic tubing. Ask at your hardware store.