Go with this one http://www.amazon.com/Sewell-Wii-HDMI-Converter-480p/dp/B0072JP56G/ref=sr_1_fkmr1_1?ie=UTF8&qid=1398017066&sr=8-1-fkmr1&keywords=sewell+wii2hdmi+480p
You don't want the adapter to upscale, let your TV do that. Set your Wii to 480P, it will reduce lag but not eliminate it.
As i'm sure you've read your best bet is to either play on a CRT, or play on a low latency computer monitor with the adapter I linked. I have a BenQ RL2455HM + The Above Adapter and it only lags 2ms more than a CRT, to me (and i'd be willing to bet anyone) that is not noticeable.
Good luck
For practical and tournament use, everyone plays on a 60hz CRT. I'm sure some CRT's can break that number, but there's no point playing on those since those aren't the standard and never will be. It's honestly best for the community to start to adopt to A gaming monitor -> Wii -> wii2hdmi adapter -> hdmi cable. That way we can move to monitors like every other competitive game, while incurring essentially no additional input lag(~2ms). Something like this can be connected any modern monitor, and allow Melee to be played offline on a monitor even without Dolphin.
This is what I use for a portable setup I made. We use it for tournaments around here and no one can feel any lag. A couple say it even feels faster but I think that's the sharper visuals from my monitor
If you use a Wii to play Gamecube games, you can use a Wii2HDMI converter to make your Wii output 480p over an HDMI cable (after changing from 480i to 480p in Wii settings). Keep in mind that this isn't true HD (which is anything 720p and above), but it should clear up any muddy glare.
For specific Wii2HDMI converters, I recommend the Sewell Wii2HDMI brand (amazon), which has been tested in an article I will link at the bottom. However, it seems to be out of stock as of right now.
You can search "Wii2HDMI" on Amazon or whatever online store you use to find a similar model. I recommend a model that does not perform upscaling, which means finding one that outputs 480p, not 720p. Let the TV upscale the image instead. However, looking through Amazon's catalog, I don't see very many that output unscaled 480p (some don't even specify a truly 480p output), so getting a 720p/1080p upscaling Wii2HDMI converter is fine.
Also, I would recommend a gaming monitor in order to minimize display lag that can ruin timings. For general-purpose gaming, I recommend either the BenQ RL2455HM or the BenQ RL2455HM. Both are the same, except that one is 24 inches and the other is 27 inches.
If you choose a gaming monitor, I also recommend getting headphones or a stereo speaker system. The speakers in my setup is the Logitech Speaker System Z313
Here's a quote for total costs.
Wii2HDMI + {monitor} + Speakers + HDMI cable
RL2455HM (24 inch) = ~25.00 + ~180.00 + ~40.00 + ~8.00 = $253
RL2755HM (27 inch) = ~25.00 + ~260.00 + ~40.00 + ~8.00 = $333
If you're looking for details on display lag, you can refer to this Smash Bros article and this Smash Bros post. A Sewell Wii2HDMI + RL2455HM has 2 ms more display lag than a CRT TV, which is almost nothing because a 60fps frame is 16 ms per frame.