I am looking for a small amp to practice with in the basement while the rest of my family is asleep upstairs.
 
Here's what I am looking for:
 

• Sounds - all I really need is a good clean and good lead sound.  

• Line In - for when I want to play with a drum machine or MP3's.

• Effects - Anything more than reverb is icing.

• Connectivity - Nice but not at all necessary.

• Batteries - Nice, but not necessary.

Any opinions would be greatly appreciated.

A Fender amp from the Mustang series or a Roland Cube would both fit your needs. The Micro Cube runs on batteries if needed and both have headphone jacks for quiet practice. The Fender has USB connectivity to their software via computer.

I love my Blackstar http://www.sweetwater.com/store/detail/ID15CombowFS
 
I paid a little less but didn't get the foot switch which I now regret. 
 
I played in a 5 piece rock band and it was LOUD. Don't let the wattage fool you. So it's not only my studio and practice amp I use it at gigs. I also have an old 74 Princeton and this is a close match tonewise and volume, but it lighter. 
 
When recording I can turn the master volume right down or off so perfect for what you want to do. 
 
The variety of tones is amazing and then the effects are top notch. The front controls take some getting used to , but you can dial in just about anything you have in your head. Then that can be saved to 12 patches easily recalled with the front buttons,, or better yet the foot switch.  With the USB to a laptop you can use the software to set it up and it gives you more control over the effects and then there's over 100 presets available.  
The day I bought it I tried it side by side with all the major brand modelling amps and it was my pick because of it's tube like punch. 
 

Depending on your circumstances, you might also want to checkout the Amplifire.
http://atomicamps.com/amplifire-pedal/
 
You can find them used on the Gear Page... for not much more than a practice amp.
 
You could use the Amplifire for practice (headphones), playing live thru PA, or recording.

I've been seeing good reviews of the Boss Katana amps from people with extensive amp / amp modeler collections. I'd look into that. Quilter amps are getting good reviews as well, but are more expensive.

The "while sleeping" makes me agree with Jim's suggestion, depending if you are going to play "as an amp." You also do not need to go new with things either, as a lot of old amps/pedalboards are still highly viable options.

Love my Yammy THR10.  It really makes these sounds even without the tennis shoes
 

+1 for Blackstar.
 
For what you're describing, the Fly 3 would work great. I love mine. I also picked up the Fly 3 Bass amp. I also use it for checking mono compatibility and for playing my phone through when I shower. $60.
 

 
https://www.blackstaramps.com/uk/ranges/fly
 
http://www.sweetwater.com/store/detail/Fly3

I love my Fender Super-Champ XD, a little tube amp with a nice sound of its own and some fairly decent modeling presets on Channel 2. Some basic in-line effects but no real control over them other than level.  No line in or batteries, though, and it wouldn't work too well when others are sleeping. Oh well, never mind.
 
https://www.amazon.com/Fe...mplifier/dp/B001L8KE06
 

Musician s Friend has the SDOTD VOX AC4 tube amp on sale right now for 199.00