While it is definitely fair (and a good idea in theory) to copy your existing library of VHS tapes to DVD, it's not as easy as it would sound.
It's not as simple as copying a CD on a computer. Analog video signals are very chaotic, and the analog-to-digital (VHS-to-DVD) process requires a number of costly tools to do a good job. A consumer VCR -- be it new or worn out -- is rarely going to work well. Most consumer DVD recorders are very touchy about copy protection (artificial video errors purposely added to tapes), making conversion impossible.
At minimum, you generally need a time base corrector (TBC) between the VCR and the DVD recorder. That means the combo units are out. The combo units were made so you could play/record tapes, and play/record DVDs, but separate from one another. It was never intended to copy VHS tapes to DVD, even though some manuals state it can. The manuals lie, and were likely written by non-engineers.
For the same $200+ it would cost you to buy a TBC -- not to mention the cost of DVD recorders, new VCRs, etc -- it's generally better to just buy the DVDs. For one, they'll look much better. If you want to go the budget route, buy used.
Amazon.com and eBay.com have tons of used DVDs available. I often buy used DVDs off
Amazon for as little as a penny ($0.01) plus $2.98 shipping, making a disc about $3. I often get TV series box sets, used for about $10-15 each. That's a fraction of the cost of what discs cost new.