Starting with the source...
Video may be interlaced -- generally leave that alone. It may have had telecine applied, which is a process of adding frames to make 24 fps video comply with the NTSC std. of 29.976 -- you can attempt IVT [Inverse Telecine] but it may/may not work, & when it doesn't can look worse. Video may also have had Pulldown applied -- rather than add frames [i.e. telecine] mpg2 files can have flags inserted that say repeat this frame, then that one to mimic having an actual 29.976 fps... It pays to get rid of those flags, but ONLY if your final video is encoded at 23.976 or in some cases 24 fps. There's little reason to bother removing pulldown if your mpg2 encoder's just going to add hard frames anyway. It gets tricky when/if your software or even graphics drivers attempt to detect & remove pulldown automatically, & it gets tricky depending on how your software treats 23.976 fps vs. 24 fps -- sometimes it's different & sometimes the same. Always Test with short clips 1st.
IF you're working with something like NTSC DVD video you can use DGIndex [ http://www.videohelp.com/tools/DGMPGDec ] together with AviSynth to import 29.976 fps mpg2 at 23.976 fps, removing pulldown, though you're limited by not all apps opening or using AviSynth files -- VirtualDub works great, but your encoders are limited so you may need to create an intermediate avi file you'll encode elsewhere. VFAPI can create a fake .avi file that most anything will open & use [rather than trying to open an AviSynth file directly], but VFAPI is 32 bit & getting it to work in 64 bit Windows is a bit of a challenge, though it is possible. Apps like Vegas will normally just remove pulldown when you import the mpg2 file.
AVC/H.264 video doesn't have a lot of timing info, so using it as a source video can be iffy. Apps like Vegas will import AVC in a .m2ts file just fine -- Roxio will import AVC in a MKV file -- and there are ways to use AviSynth to import it into apps like VirtualDub, though they're not pretty & don't always work that well. Tsmuxer is the std. free tool to both put AVC into a .m2ts file & strip it out of one, but in somewhat rare cases it can & will drop full or partial frames. Other apps I've tried, & I've tried a Whole Bunch, can shorten the video by skipping frames, throwing off audio sync -- when it skips groups of frames at different places in the video, good luck fixing sync then. At any rate, get the *exact* length by for example opening the AVC in a player, & compare that to the length when you import that AVC into whatever app -- if they don't match don't bother going further. To handle AVC [& formats like VC1] tools like ffdshow & the LAV Filters *may* help.
As far as encoding speed...
Specialized apps like A's Video Converter [ http://www.videohelp.com/tools/As-Video-Converter ] can be amazing, but for some formats more than others, & they aren't as easy or flexible, while quality usually suffers... it works by using the video card's built-in video processing capabilities. The average GOTD video converter OTOH does a good job encoding video to 720 width or smaller AVC. Nero Recode does a great job encoding DVD type video to AVC as well, & can do a lot of neat tricks like include the subtitles. For HD, the Sony AVC encoder in Vegas is the fastest high quality encoding I've come across, at slightly over realtime on this PC [a 2.5 hour video takes ~ 2.75 hours]. And that's at Blu-Ray spec. Nero by comparison takes twice as long, or longer, & Roxio while faster than Nero, doesn't have much in the way of output formats -- I'll use Roxio if I have to but render to highest bit rate HD mpg2 as an intermediate. X264 via whatever front end works well -- it's just not as fast.
There are a lot of tools for repairing or re-writing video files in case you can't import or open the file you want -- none are perfect so test anything that looks like it might work. Ffmpeg can do some neat tricks when it comes to re-writing a video file, e.g. moving the contents to a .mov container, & *sometimes* that works. There are also a bunch of tools revolving around mkvtoolnix, & those can come in handy for stuff like AVC.
Finally, someone asked in one of the comments about quality...
Filtering video in something like AviSynth &/or VirtualDub can help, & they can probably do a better re-size than most alternatives regardless the price. Starting with the best possible source is critical -- convert Blu-Ray video to DVD & you'll see what you thought was OK video is more like what the studios thought they could get away with. Use the best encoder you can at its high [or highest] quality settings -- x264 for example can be set to be extremely slow, but very high quality, which is BTW the normal trade-off. While you're at it research that encoder to find out what other settings can make for higher quality results. Allow enough bit rate for your encoded video -- DVD-sized mpg2 video can be near lossless with a bit rate ~25-30, at the DVD max around 9-9.5 it can look extremely good, at a bit rate of around 6 it might look OK. Variable bit rate encoding uses a higher bit rate when needed, balanced by lower bit rates when it's not so critical to keep file size within reasonable bounds -- you can often set minimum, average, & maximum figures, so customize all 3 based on your content. Going beyond those points requires a bit of research IMHO, learning about things like the colorspace your original source uses, & doing your best not to compromise quality by avoiding conversions as possible, using the best methods for any colorspace conversion when it's not. And tying into what I said about the source being the most critical component, the more data you have the more you can spare... on your way to a final 320-720 width video you can process a 1080p source quite a bit more than a video already at your target size, so use the largest frame size source, & keep it at that larger size as long as possible, saving your final resize to just before or during final encoding.
