I think one thing to consider is whether you really like to "tweek" and play around or do you want to just buy something and let is spin records.
Simple non-suspended tables like VPI Jr's and Scouts and Rega's are simple to set up. Set it and forget it. Linn's have a reputation of being harder to set up and harder to keep set up, but people who love them really love them. Some other suspension tables have the same rap. Rega tonearms don't have built in VTA which is another tweek factor. I have heard VTA adjustments in real time and I can attest that yes it does make a difference but do I miss it at home on my Rega P25 - no, not really. I also heard a Linn table vs another table wtih both tables having the same tonearm and cartridge mounted on them and the Linn blew the other table away. So yes, the table itself does make a signifacant difference too.
Cost is obviously also a factor. If you are the kind of person who likes to buy, but inevitably upgrade then buying a used Rega, Linn or VPI for which there are current upgrades and accesories might be good. On the other hand if you fall in love with a used SOTA or Oracle I think you could do a lot worse.
Lastly there is the aesthetic element. I like more traditional designs - wood plinths and the like. No cast bases or air bearings for me.
On the cartridge front there are also many good options - Shure V15 are surprisingly good and more indestructible which is good if you are clumsy, have kids or cats or a spouse who is a compulsive cleaner... Dynavectors, Shelters and a variety of others are all good. You will find supporters of nearly all the top brands on these forums and elsewhere.
Lastly is the issue of cartridge output. If you go low output moving coil you need to make sure your pre amp can handle the input. I don't know the Levinson integrated that you mention and whether it has a phono stage or not but if it doesn't you need to get the whole phono stage and not just a step up. I won't mention all the phono pre's as you will find various discussions here and elsewhere. Try www.audioasylum.com for additional insight.
At this point you've got 5 significant variables (table, arm, cartridge, pre amp and price) so yes the combinations and permuations are endless, but that is part of the fun...
Good Luck,
Phil
PS I settled on a Rega P25 with a Shelter 501 Mk II. I don't really want to tweek the thing I just want it to be reliable and make good music.