There's a few ways to go about it, depending on how far you're willing to go. There are converters for the job that can really clean up the signal, but their ability to handle consoles can be difficult to measure in part because of the input lag as mentioned. Your TV also factors into that as well, so you might want to cross-reference the TV you're looking at with www.displaylag.com and its database.
Pretty much everything up until the Dreamcast usually had a better option for video outputs, save for a few exceptions. Actually the ideal signal to get from said would be RGBs or as Europeans know it, SCART. We in America got screwed out of ever seeing this available, but for the most part the consoles still can provide a signal with the right cable. And unlike RCA or any other such, modifying the RGB/SCART for the region you need isn't that hard. It's a huge plus if you know how to solder.
Finer points that are console-specific:
•I am aware of component video mods being able to be done with the NES, but they all require some hardcore soldering, a custom PCB to piggy-back the NES's original video chip, and components borrowed from the Nintendo PlayChoice10 platform. Otherwise your best bet really is the Composite A/V, as only the French releases of the system actually had a SCART connector and cable made.
•standard SNES's support the RGB cable no problem. SNES jr's would need some soldering to restore the capability, as Nintendo rather inexplicably cut it out of the system, and even cut out S-Video capbability. Thankfully, a Component Video mod is much easier on this system, especially with the right encoder chip on yours. Again, soldering is required... but if you've got the right encoder chip, it literally would just be three sets of wires and three RCA jacks to match (plus another two if you want to wire the stereo audio as well).
•Like the SNES Jr., the N64 inexplicably disabled RGB out. But like the SNES, it's simple to re-enable, and it can use the same cable.
If you go this route, you've already got the better part of getting the best signal out of the console. Now the trouble is finding a way to hook it so the TV can understand, lol.
A lot of modern TV's will not understand the 240p that the old systems (and this includes some N64 games - KI Gold for instance actually would flip-flop between 240p and 480i on the fly as observed by some video-philes). The cheap way to find t his out would be with a simple RGB-to-YUV converter. It takes the RGB/SCART at one end and outputs component video. You'd probably want a separate breakout/pass-through adapter to get the audio out as well. The good news is it's relatively cheap, and compared to anything else won't add any additional lag. The bad news is that - again - modern HDTV's might not even understand such a low-res signal. if it does, it'd be a very cheap way of getting the sharpest and purest picture possible. If not, well... you'll need to fork over some more bucks.
On the pricey end, the be-all, end-all of gaming converters for such things is the
xrgb mini. It'll run about $350(+), but I've yet to read one bad review. It's ludicrous how fast that thing is, and how impressive it cleans up the look of games on a modern TV.
Again, your light gun stuff won't work on any HDTV's nowadays, which is a shame...