#2 and #3. All up to you. Depends on how well you know how to manage a server, then #3. If you want someone else to do it for you and you just pay them then #2. Cloud is good at Load Balancing. 50k to 100k registered users is not a lot. How many do you estimate being online at the same time?
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As always, I don't exactly recommend VPS's for these types of applications.
I have had my fair share of VPS's, and even though they were great at what they were designed to do, sometimes I would simply just receive ridiculous amounts of lag and so forth (It's on a server with other people, remember that) and that lag wouldn't go away for a while.
I recommend Dedicated Servers for a website like this, though truly I would recommend the service MediaTemple as your front end and a back end dedicated server using tomcat.
The way it would work is you would design your front end to run via PHP on the MediaTemple grid server, that way your users wouldn't see a front end down time when one would happen. After that, find a budget dedicated server and set that up to run your daemon in the background, have your PHP front end negotiate with your Java backend via HTTPS or some similar protocol, and you're set to go.
That way, if you happen to get down time, your entire site wouldn't go down, just your frontend/backend.
A VPS server sounds like the place to start for my two cents. If you pick the right host you can grow the server as your site grows. I started with a small VPS for my baseball card case break forum site and it is running very smoothly and my host is taking care of me and server nicely. As site grows I add to server. At some point it will be smart to switch to a fully dedicated machine but why waste the money up front when you just need registered users to grow.
VPS is enough for starting small business, but if your website grows up then you can upgrade to dedicated servers. Since it is an auction site i guess you won't get traffic spike much. So go with VPS hosting itself.