If I wanted to ballast an 18 watt LPS lamp and I don't want to spend $100+ on an L69 ballast, what can I use?

Try full power F20T12, but may need some ignition aid at 120V (parallel starter,...)...

Those cheap little instant start electronic ballasts for 14-20 watt fluorescent lamps work well.  I've also tried single lamp magnetic trigger start ballasts for 14-20 watt lamps with success.

Ok cool, thanks.

You're not supposed to operate HIDs at high frequency as it may cause resonance and damage. Not sure if it applies to LPS.

HID electronic ballasts use square wave to drive lamps at around 400Hz.

LPS are technically not a HID, they are (falsely) listaed as HID only because of their expected use in street lighting...
Technically they are very close relatives of fluorescent tubes, the only difference from fluorescents is the use of sodium as an active discharge material (instead of mercury) and no light conversion (as the sodium already radiate in visible, while mercury in UV).
Otherwise both fluorescents and LPS are low pressure discharges, so in both the arc is rather cold (way below few 100's of degC) and fill the whole cross-section of the tube, while it's shae is forced by the tube wall.
In true HID the arc is very hot (few 1000's of degC) and located only in confined space (filament), it's position is given by the balance between it's "desire" to be as short as possible on one hand and convection draft "trying" to blow it upward. The arc tube is then designed so, the arc is not touching the arc tube wall.
The high frequency operation, what widen the arc (and concentrate it to the perimeter of the cross-section), so on low pressure lamps increase the efficiency of generating the radiation (as the generated light does not have to pass so long trough the gas, what is opaque to it).
The same effect cause the arc of a true HID to become unstable and move closer towards an arctube wall, so overheat it. But as on low pressure lamp the arc's shape is already formed by the arctube, it can not influence it further.

I've had success running a 18w LPS with a F32T8 Instant Start Ballast before, I also was able to run them with a European F20 choke with a step up and a starter parallel to the lamp but using a 120v choke didn't work for me.

I would be running it on 120V 60Hz. Was looking on ebay and there are some cheap F20 ballasts both magnetic (preheat and trigger start) and electronic. I'm also thinking I could find some inexpensive ballasts at Lowe's or Home Depot, they might be elctronic but that should work, right?

The only problem with LPS is the correct power: LPS are extremely sensitive to underdrive - their efficacy drop very severely. They "consume" certain power only to heat the arctube up without radiation of any light and only the rest is converted to light.
The electronic Instant start (with single wire to each lamp end) are the best, as these provide enough OCV for ignition and seem to survive the open load condition (should the lamp fail). Then any electronic with EOL protection more advanced then filament fusing should be OK, you only have to determine, what leads carry the power and what are only for electrode heating. Then connect 10 Ohm/2W resistors instead of the fluorescent filament.
With the Cheepeese selfoscillating electronic ballasts you would have to use 6V/0.5A incandescent lamps instead of the resistors to protect the ballast in case the lamp fail (the excessive current evaporate the filament and as it break, it stop the ballast)
Magnetic ballasts are OK, if they are able to provide enough OCV, so on 120V only RS are in the game (F20T12 preheat have too low OCV)...