Keep in mind that the LM1875, while an excellent and simple choice,
requires a minimum Power-supply of ~16-Volts for stable-operation,
which will then produce around ~7 to ~8-Watts of Output-Power,
and only costs around ~5-Bucks from DigiKey-Electronics.

Up to ~30-Watts of Power is feasible with a much-higher Supply-Voltage.

An SMPS from a LapTop-Computer would be a great choice for a Power-Supply for this application,
and may be able to generate about ~10=Clean-Watts of Power with this Chip.

With a carefully selected Speaker, and a properly designed Cabinet,
this setup could be a very respectable Guitar-Amp,
which is also capable of handling small Gigs.

If You think your Wood-working chops might be better than your Electronics expertise,
You could build a serious, real, premium-quality, ~25-Watt-Guitar-Amp for just over ~$150.oo,
by ordering Cabinet-Plans from Bill Fitzmaurice,
and 2-Speakers, and a Digital-Amp, from Parts-Express.

Note ........
The Amp uses the "Chinese-Power-Rating-System", don't believe it,
in "Real-RMS-American-Watts" the Output is maybe around ~25-Watts or so.
This setup can easily generate over ~100db of "clean" Audio-Output,
and substantially more when over-driven into Distortion.
The Speakers can handle ~10X as much Power if You want to up-grade the Amp.
.
.
.

 

Here is a project using the LM1875 on a PCB board layout.

https://www.electronics-lab.com/project/20w-audio-amplifier/

You can also buy an LM1875 kit from Amazon. (While you are on Amazon, look for other low power audio amplifier options.)

 

Another choice is TDA2050.

https://www.amazon.com/HiLetgo-TDA2050-Amplifier-Digital-5W-120W/dp/B0CDWTL57H

 

Low power (7W), low voltage (3-18V) single supply, bridged output (no output capacitor) audio amp TDA7266M.

 

Another choice is TDA2050.

https://www.amazon.com/HiLetgo-TDA2050-Amplifier-Digital-5W-120W/dp/B0CDWTL57H

Thank you for all of the suggestions. With any of these, what's the best/preferred method for connecting a 1/4" input jack?

 

I am giving you relatively simple options, single channel, 20W min, 12VDC supply.

Use a chassis mount 1/4" jack. Use shielded audio cable to connect from the 1/4" jack to the amplifier module.

 

For best results, You may need to add a Pre-Amp Op-Amp, before the Main-Amplifier.

I'm not exactly sure what the ideal-gain should be,
but a generic Guitar-Amplifier normally has to be capable of directly Amplifying a Guitar-Pick-Up.
This is probably in the range of ~80X to ~150X-Total-Amplifier-Gain for full Amplifier-Output.
This Gain figure is highly dependent on the maximum Output-Voltage that the Amplifier is capable of.
.
.
.

 

Good point. A signal preamp can be a simple single stage BJT or FET class-A amplifier.

 

A serious bit of caution here. That TDA2050 is a device, not a module with terminal connections An amplifier using it is not tha same as the device alone.