I think you need to start from basics.
Lets try to establish two points
You can use DVD disks in of two ways
1. As a dvd video disk. As LV426 has explained, this is a disk that you can put into a dvd player and it will play a film, just like one used to rent from Blockbusters, or buy from Tesco et al. This is DVD-Video. Films on this disk must be encoded using mpeg2 (.mpg), the disk has a specific directory structure, and the film is split into one or more .vob files. Generally, you have to use a software program to create this disk, c/w menus and navigation buttons for it to play back.
2. As a dvd data disk. Think of this as a 4.7GB removable data drive, like a USB flash drive or a large capacity floppy disk - because this is what it is. With Windows 10 you can just drag and drop files to it, and Win10 will happily write away, although you may need to "close" the disk manually.
Such a disk will not do anything when put into a DVD player - or the vast majority of them. However, because you can write any type of file to it, you could write one or more video files (e.g. my_holiday_film.mp4, a-home-video.mpg, a-nother-video.avi my-karaoke.mp3 etc) These can be played back on a PC just like being on a hard disk. And some dvd players, consoles, etc will play back these individual videos - or .mp3 in the example
These two types of DVD are wholly different, and you need to be clear which you are creating.
I do not mean to be condescending, but your posts show a massive lack of knowledge over video standards, video capture, encoding and transcoding (and Nero is transcoding, which is where some of your issues are coming from), and the software. And unfortunately, you need to know the basics for this to understand how to get the results you want, or the limitations imposed on you from your choice of capture method, encoding/transcoding, and tools.
To address a few points
.avi does not produce 'huge' files. It is a container format. The size of the file depends on the encoding format and the compression settins.
VirtualDUB - one of the most powerful video tools from 'yesteryear', but it is not a tool for beginners. It is not a dedicated video capture tool.
Handbrake - a reasonably powerful encoding/transcoding tool with a simple front end so it can be used by all. But, you do need to have a basic grasp of video standards, the tradeoffs of higher compression/smaller file/lower quality vs lower compression/larger files/higher quality.
Encoding - taking uncompressed video and encoding and compressing, e.g. to mpeg2, mp4,
Re-encoding - recompressing file in one format to the same format with different options, e.g. uncompressed (but encoded) mpg and exporting it in compressed format
Transcoding - taking a video file compressed and encoded in, for example mpg format, and re-encoding in another, e.g. mpeg2 to h.264
This is very overly simplified.
mpeg encoding, to use an example, has a huge variety of options, allowing for a very fne control over the output file. BUT accessing these options depends on the software used. Simpl, fee software possibly only allows you to choose PAL/NTSC, some resolution options, a simple size/quality slider. Other, such as Mainconcept Encoder, allow you to specify resolution in pixels, frame rate, number of passes (two always better than one), sub-pixel movement, search width, search height, spatial or temporal search, quant matrix, 4:4:4 through 4:1:1, etc etc etc. Its complicated, encoding takes time, but the results are worth it. TEMPGEnc encoder is another example.
Again overly simplified and just a taster of what isavailable.
Nero Recode is a cheap, "video for dummies" that tries to do it all with a very simple interface. And the results reflect this. For some video, it can produce a decent result - provided nothing much is asked of it. But, it can also produce nonsense results, especially when transcoding is required.
You might notice that all the cheap/free software offers very little in the way of control of the conversion process (ie quality - very low, low, medium, high, highest). Its to keep things simple. But these generally only mean "how much compression - huge, a lot, average, some, almost none") with absolutely no control over the fine tune options that say Mainconcept offers:
If you take any given source file (uncompressed) and run it through crapware and mainconcept, the resulting file from Mainconcept will be superior in every way, and even produce a smaller file.
Why? Because you can control the entire process, every encoder option, colourspace compression, number of passes, bit allocation etc.
I'd suggest having a gander of the FAQs and guides on forums like videohelp.com, doom9.org, digitalfaq.com - but note I said read, I'd really advise against for help until you get the basics.
And also - not criticizing some of the software as you have here - you will be flamed if not banned.