Hey, forget about it!
Ha, just kidding.
There's several inexpensive headphone amps you can get for ~$30, sometimes more or less, depending on what's on sale. Shop online, check the GC brochure or the AMS catalog, I'm sure there are a few to choose from.
F/I, I got a Danelectro headphone amp for about $18 at GC, marked down from $29, and the following few weeks I saw the same unit there for ~$9.99. The Danelectro headphone amp has cheesy reverb and cheesy distortion built in, but it's functional enough.
>I think there's a line of headphone amps called "Pocket-Rockit", or something like that, & I think that IBANEZ has a line of small, inexpensive headphone amps, so shop around.
>Also, Tascam has a nice headphone amp+CD player that's marketed as a "practice headphone amp/phrase trainer", all for about $100. You can listen to/practice along with your favorite CDs, all onboard the same unit.
>I have a vintage headphone amp, that's pretty neat, called the Yamaha MA-10, which is a box-unit, with Gain, Bass/Mid/Treb and 2-headphone outs, as well as handy RCA & 1/4" stereo connections for everything, [Line In/Out, Mon In/Out, Aux In/Out],... making it a handy little unit for the home studio.
However, this being said, there are still other options, if you shop around. I'm not up on all of the very latest products, and there may be something suitable for you that I have not mentioned.
Q: If your guitar amp has LINE OUT but no HEADPHONE OUT, then to utilize the LINE OUT, wouldn't your amp have to be turned up to a nominal level, producing all that unwanted noise pollution?
A: If your biggest concern is noise, or being quiet, then I think using your amp & line out is "out",... unless there's some other detail I missed. However, for normal purposes, the LINE OUT tap from your amp can be really handy for recording.
Also, IMO worth mentioning, is that a NICE/Used Tascam 244, 246, or 424mkII can be bought for around $150-$200 on most days, and that would provide you with all the inputs/outputs & headphone feeds you want. Well,... actually, the 244 & 246 both have two headphone outs, and the 424mkII has only one, but it's enough if you're working alone. PLUS, if you go the Portastudio route, then you'll have plenty of auxilliary mixing capability, up to and including 4-track tape production, right on board.
Funny, but a while back I saw an entire Tascam M30 mixer sell for exactly $56 on Ebay, and jfyi the M30 would give you full-blown 8x4x2x2 mixing capability, complete with 6-XLR inputs and 2-HiZ-1/4" inputs. THAT would be the TICKET, for a mere $56, which is the lowball deal of the season, but the Tascam M30 typically sells for about $100-$150 anyway, so on most average days this is a great deal.
Anyway, that's my input on this topic for now. Hope it helps.
Good luck.
