The cheapest option is to use the composite output, so it's compatible with any monitor that supports composite but it's only black and white.
Or if you have the A520 modulator (about $25 on eBay), you can get a color image through composite, RF (not recommended), or modify the A520 for S-Video.
If your TV has a standard definition tuner, you may also be able to connect your Amiga 500 through a third party RF Modulator (about $15) but again this is not recommended.
Next up is a simple HD15 adapter ($10), but it outputs a 15kHz horizontal scan rate (VGA standard requires 31 kHz) so it only works with a limited set of modern LCD monitors.
Next is Kipper2K's S-Video adapter, but these are difficult to come by. Or make your own.
An option for component video is the GGLabs A520HD ($80 or build your own with the supplied Gerbers). Like the other options above, it doesn't have a framebuffer so lag is minimized and the picture is sharp, but the Amiga outputs a nonstandard sync signal and so this may not work with all monitors that support component video. To test your monitor, hook up the composite output from your Amiga to the green ("Y") component jack on your monitor and see if you get an image.
On a budget, the ubiquitous Chinese SCART to HDMI adapter (it's sold under different brand names on Amazon and eBay but I think they're all the same) is probably your safest bet. It has good compatibility and gives a good picture but the framebuffer adds some lag so it may not be the best option for fast paced gaming. Just add an Amiga SCART cable.
If your monitor takes VGA or component (YPrPb), Tim Locke's answer is a less expensive alternative ($20-25) but requires a little DIY. It has a framebuffer so compatibility is good. Similarly, the Wei-ya ACV-011 ($65) takes some DIY and trial and error but produces a sharper picture with less lag.
And finally, the Indivision ECS, OSSC, and Micomsoft Framemeister XRGB-Mini provide the best picture quality and the lowest lag.
But please keep in mind that the better-than-composite options won't look right with games that take advantage of composite artifacts to produce more colors. Virtual Karting 2 is one example.