Monitor

It will work with LCD TVs. (Better, in fact, than with CRTs.)

It will not work out-of-the-box with typical PC monitors that only have a VGA, HDMI, DVI and/or DP input, but you can get yourself a composite-to-HDMI adapter; those typically sell for less than 5 Euros on AliExpress.

Right off, the disclaimers and caveats: You're actual millage may vary. Low end upscalers are entirely a crap shot. They're cheaply made and the output quality is wildly inconsistent so, at very best, you're going to get passable video. Currently, there are only two real solutions to the problem are the Framemaster or the Open Source Scan Converter (OSSC), unfortunately they are also fairly expensive.

The first part of the equation is the Television or Monitor your using. I tested straight composite video on the 3 panel TV's:
Panasonic Viera 54" Plasma HDTV - 2009
RCA 32" Full HDTV - 2012
Insignia 40" HDTV - 2014

The Panasonic was the worst of the 3, the Insignia did a reasonably good job, and the surprise was the RCA which did a good job displaying the Basic Engine.

The Second Part of the testing I did was with a number of relatively inexpensive Upscalers:

Note: none of these retained a 4:3 aspect ratio

enKo Products Mini Composite to HDMI:
There are a number of "Best of" reviews out there that list the enKo, often in reference to retro gaming, at or near the top if it's class for these converters, but I have to say my experience is that they are closer to the bottom of the barrel. The picture was dark, colors washed out, and, most annoyingly, there was a constant repetitive beeping in the background of the audio.

GANA 1080P Composite to HDMI:
Better then the enKo, but a lot of color bleed.

IBIT SCART to HDMI:
I'd bought the scart converter to use with a number of other retro systems and as such it doesn't have a composite input so I use a CESS RGB Scart to composite/svideo adapter with it. It does a good job of upscaling, some slight color bleeding. The IBIT tied with the Etekcity.

Etekcity® Composite to HDMI:
The Etekcity did a good job upscaling, some slight color bleeding, and was a tied for image quality with the IBIT... though personally I do like the Etekcity a bit better.

The third part was the using a line doubler.

the Retrotink is unique in that it isn't upscaling to HDMI 1080/720 but rather, takes 240p/480i, 288i/576i, NTSC and PAL and PAL60, and outputs it to HDMI at 480p/576p. The Retrotink does a good job, snd it does keep the 4:3 aspect ratio, but the quality of what you're going to get is going to be very dependent on the TV your using as it just converting the video into a format that's more compatible what HDMI is supposed to handle. For what it cost, an OSSC might be a better option l, especially as it's only slightly more expensive.

The fourth part if testing was vga conversion:

I have couple composite to VGA converters I wanted to try and, as with the HDMI upscalers, they produced images that were not nearly a clear and free form color bleeding as I would have like. I used a couple 4:3 LCD displays and I tryed 2 converters, an Ambery AV-8, and one of the inexpensive component to VGA common in eBay and Amazon, and both has very similar results. The cheaper generic converter has one big advantage as you can adjust its image though an onscreen menu.

As I was trying the VGA converts, I wondered what would happen if I feed the HDMI for the upscalers though the simple HDMI to VGA converters I use with my Raspberry Pi's. The results were a real surprise - the best image quality I've was able to get so far. I believe this case because monitors are far better at rendering then most televisions. The Etekcity upscaler with the VGA adapter had what I think was the best combination. One of the big bonuses was that it brought the aspect ratio of the HDMI output back to 4:3, and the next test to see what I does on a newer wide monitors.

Next step what I have a chance it to write a test pattern program so I can make some comparison screenshots.

I have made a color bar test pattern based on data from https://en.wikipedia.org/wiki/SMPTE_color_bars. As an aside it is also a test of the DIM, RGB(r,g,b), and GOSUB w/ labels.

Program listing:
100 REM color bars
110 REM https://en.wikipedia.org/wiki/SMPTE_color_bars
115 REM using the 2nd color chart
120 CLS:SCREEN 4
125 GOSUB &colorset
130 x=0:y=0:x1=45:y1=132:cc=0
140 FOR x=0 TO 270 STEP 45
170 RECT x,y,x1+x,y1,c(cc),c(cc)
175 cc=cc+1
180 NEXT x
190 REM small row of rectangles
200 x=0:y=132:x1=45:y1=145:cc=0
210 FOR x=0 TO 270 STEP 45
220 GOSUB &fifthrect
230 NEXT x
231 RECT 0,145,160,200,white,white
240 GOTO 240
250 &fifthrect:
260 REM 1/5 size rectangles
270 RECT x,y,x1+x,y1,d(cc),d(cc)
280 cc=cc+1
290 RETURN
320 &colorset:
330 gray=RGB (104,104,104)
340 yellow=RGB (180,180,16)
350 cyan=RGB (16,180,180)
360 green=RGB (16,180,16)
370 magenta=RGB (180,16,180)
380 red=RGB (180,16,16)
390 blue=RGB (16,16,180)
400 white=RGB (235,235,235)
410 black=RGB (16,16,16)
415 DIM c(8)=[gray,yellow,cyan,green,magenta,red,blue,white,black]
417 DIM d(6)=[blue,black,magenta,black,cyan,black,white]
420 RETURN