in terms of ranking high fast for a keyword in search engines. lets just use weight loss as an example. if my site was about weight loss and i wanted to get in the first page of Google quickly would it be better to buy a old health realted website (rename it and do a webpage overhaul) or just start a new weight loss website? does age matter? would a 5 year old site with zero SEO done be the same as starting a new site? assuming a 5k budget for SEO either way. thanks!
I would recommend starting a new website and buying an old domain (how old will depend on your competitions domain age) that contains your keywords.
An old domain would be more accepting of backlinks. A new domain would take longer. But if you get an Exact keyword domain name it may help. But are you trying to build an authority site or just a one page salesletter type site?
If you are talking about a monthly budget, then yes you can target some pretty good keywords at that budget. If you are talking one time, then probably not. That budget cannot get you top positions for most keywords. As for the age question, starting a brand new domain and website is very different than buying an existing website (of course many metrics come into play when looking to buy existing websites/domains). Indexing and ranking can be accelerated with an existing website if it has the proper requirements to do so.
I'd definitely recommend you start with an unregistered domain and then SEO it. Just because you're buying an existing site gives you no guarantees - especially since you're going to make some signficant changes: probably a change in IP, definitely a change in content etc. If you can find a suitable unregistered domain that has some existing links then great, and then your 5k is best spent on building good links instead I think.
It can provide guarantees if you do your research right. Buying existing websites/domains can be great for seo, proper research is needed before of course. An IP change is not a significant change in seo at all. Search engines understand people change providers and move their website around sometime. As long as components remain the same, shouldn't affect seo.
Either way New site Old site You won't get quick rankings Especially in a niche like Weight Loss ....