Good to see someone's chimed in about Lucene - because I've no idea about that.
Sphinx, on the other hand, I know quite well, so let's see if I can be of some help.
Result relevance ranking is the default. You can set up your own sorting should you wish, and give specific fields higher weightings.
Indexing speed is super-fast, because it talks directly to the database. Any slowness will come from complex SQL queries and un-indexed foreign keys and other such problems. I've never noticed any slowness in searching either.
I'm a Rails guy, so I've no idea how easy it is to implement with Django. There is a Python API that comes with the Sphinx source though.
The search service daemon (searchd) is pretty low on memory usage - and you can set limits on how much memory the indexer process uses too.
Scalability is where my knowledge is more sketchy - but it's easy enough to copy index files to multiple machines and run several searchd daemons. The general impression I get from others though is that it's pretty damn good under high load, so scaling it out across multiple machines isn't something that needs to be dealt with.
There's no support for 'did-you-mean', etc - although these can be done with other tools easily enough. Sphinx does stem words though using dictionaries, so 'driving' and 'drive' (for example) would be considered the same in searches.
Sphinx doesn't allow partial index updates for field data though. The common approach to this is to maintain a delta index with all the recent changes, and re-index this after every change (and those new results appear within a second or two). Because of the small amount of data, this can take a matter of seconds. You will still need to re-index the main dataset regularly though (although how regularly depends on the volatility of your data - every day? every hour?). The fast indexing speeds keep this all pretty painless though.
Based on your clarifications, I want to divide your question into two, and answer each in turn:
How do I index words with apostrophes as equivalent to similar words without an apostrophe? e.g. mapping Moodys and Moody's to the same index term.
How do I implement auto-complete search in Lucene - i.e. given an index, find documents using word prefixes, e.g. map Moo to Moodys ?
1 is relatively easy - Use a StandardToeknizer to create a token combining the apostrophe and s with the previous word, then a StandardFilter to remove the apostrophe and s. This will convert Moody's to Moody. A StandardAnalyzer does this and much more (lowercasing and stop word removal), which may be more than you need. Using a stemmer should take both Moodys and Moody to the same token. Try SnowBallFilter for this.
Best Answer
IndexReader.isOptimized