If you are talking about Crunchyroll online streaming by chance I'd tell you to consider a a 120hz or 240hz model that is know to hadle 2:2 and 3:2 cadence pull-down well. the same is mostly true for other streaming sites too but I know Crunchyroll has some 1080p.
Consider that Anime on DVD or blu-ray is normally given a proper tele-cine'd encode to display the images in the proper cadence and the original sometimes do use 12fps doubled or 24fps content , it is mostly still encoded as 29.97 on DVD but should be 24fps on blu-ray so the better models that handle cadence changes or have know good processing will handle the fast motion scenes well and should look smooth like a animation should but it shouldn't have to look like a live action /soap opera.
Plasma sets typically handle native rate stuff pretty good if the source device passes the cadence well , the issues being that on a lot of anime that was encoded before blu-ray hit the market or the original broadcast was in 720p or 1080p . Japan didn't make the switch until just march of 2012 so a lot of the licensed stuff that is streamed is older content and it wasn't deinterlaced properly sometimes or not encoded as 24fps material.
What ends up happening is the motion of the scenes will either have artifacts or it will not be smooth because the cadence wasn't encoded properly in the material the streaming site uses.
If the stream on the Roku is just sending 720p@60 or 1080p@60 and not a native rate of the original a set with good processing can still help if it "sees" the cadence and processes it as 12fps or 24fps inside of a 60hz signal, it can help the picture look much better and smooth like a nice animation instead of just a online stream.
This is a problem with a lot of anime because of the way the animation is made some set just will not handle mixed cadence content well so scrolling text like the intros or outros will play at the wrong speed or if you are watching subs instead of dubs, the text will look to be playing at a different rate of fps and too smooth.
for some content it won't matter much but if the TV handles all the weird cadences well and it has good interpolation routines it can really help the images look better.
I personally used my HTPC to handle the processing for anime I watched and once you have the decoding scaling the images and putting out the processed frames , even most 480p encodes look a lot better versus just sending it straight to the 60hz TV I had but if the TV had 120hz or 240hz processing it probably could have been a lot easier and had better results.
I'd like to think that most plasmas will do better without needing additional processing and just be fed a good blu-ray source but having the option to process the anime with either motion interpolation or just proper pull-down that a 12hz or 240hz might handle is better than trying to use the 48hz or 96hz mode that mostly doesn't get reviewed well on a lot of plasmas.
I'm kinda in the same boat, I used to use a CRT monitor for streaming anime and some gaming but it recently died and the motion on a regular 60hz LCD just doesn't seem to look as nice. Almost everything I watch is anime or film based streaming and at first I really wanted a plasma but know it looks like it will come down to which set can handle the processing better.
All of the downsides of a 120hz or a 240hz LCDa tend to not really affect a animation in the same way as it makes TV shows look unnaturally smooth because on real film, motion has a blur at low rates like 24fps (60fps too if the shutter isn't setup for fast movement) but drawn animation really is mostly just a lot a single frames with a slight change that a artist drew to look like real motion (CGI shots are slightly different) so if the frames are interpolated it just smooths out the frames as if the animatior drew more frames themselves instead of the 12 or 24 per second.
It all kinda depends, a lot of reviewers us a blu-ray test disc or a dvd to check if a model is handling the proper pulldown methods and even still many sets down seem to handle the "strange ones" that anime tends to have a lot more than regular filmed live action and it doesn't help if the content was handled wrong when it got encoded for streaming but I'd rather have a set that gets more options to help than not if I cannot start with a good source like a DVD or blu-ray source have.
here is a link mentioning some of the unique issues anime can toss versus regular content: http://www.avsforum.com/t/206510/3-2-pulldown-what-is-it-and-do-i-need-it
is is old but the info is still proper to an extent. I'm hoping I can find a good model or line of sets that are know to process anime well instead of having to insert a OPPO or a AVR into the processing chain. I know it is typically "garbage in garbage out" but if I invest in a new TV I'd really like the option to rey and improve the picture quality versus the set only bringing out all the flaws or making them worse because it doesn't process them well enough. Ideally I'd just get all my anime on blu-ray but with the amount I watch and some old stuff never hitting the US for a reasonable price, investing in a better set is probably more worth it.
I'm actually going to demo a few sets tomorrow in person so if I happen to see one that stands out I'll chime in here again.