train from leipzig to berlin--which station in Berlin?

Is this the correct site to buy these train tickets (they seem to be much cheaper than buying them on rail europe's site)?>

Yup for sure IME but not on all trains - but obviously the ones you compared were cheaper in Germany - now scour bahn.de for SPAR fares - deep discounts only available online and should be done far in advance, as these limited in number discounted seats often sell out early and then you pay full fare.

If going the full fare route then just wait until Germany to buy your ducats - same price and you can always get on any train IME - twice hourly trains on mainlines.

Yes the Deutsche Bahn site is the correct site to buy your train tickets. Don't buy from Raileurope which takes a profit on top of the DB price. Your hotel is close to the Berlin Zoologische Station.

More commonly called the Berlin Zoo Station.

Thanks all. I thought the Berlin Zoo station was closest but just wanted to be sure. Price difference can be quite huge, which is what had me nervous.

Assuming you will take the high-speed ICE train from Leipzig to Berlin:

All ICEs call at Berlin-Südkreuz and Berlin Hbf (main station) - and Berlin-Gesundbrunnen, the latter irrelevant for you.

Going to Berlin Zoologischer Garten (which is the full correct name of the Zoo station) will require a change to S-Bahn at Berlin Hbf, included in your regular train ticket.
But: the Bleibtreu hotel is not withing walking distance from Zoo station, less so with luggage. You'd need to change to a bus there (not included).

If you can spare appr. €15 for a taxi, get off at Berlin-Südkreuz. That station is easier to navigate than the main station, never crowded, and faster by taxi to your hotel as well.

Cowboy brought a good point, your train will end in Hauptbahnhof unless you enter your specific final destination inside Berlin when you buy your ticket, which will then include the extra S-bahn ride.
The closest S-bahn station to your hotel is actually SAVIGNYPLATZ which is the station immediately after Zoologischer Garten. From Savignyplatz, you can practically walk to your hotel, just 3 blocks south of the station. The Zoologischer Garten is almost a mile away from your hotel. Any specific reason for staying at the Bleibtreu?

Thanks for the information. I ended up buying the tickets on the db site and listed the Zoologischer Garten stop as the destination because I didn't see an option to select savignyplatz (unless I missed it). As I now have the ticket, is it ok for me to stay on the train until savignyplatz? Am I risking a fine if I do that? Does someone check?

Does the S-bahn still run as frequently during the day? I read about some major work being done due to safety problems.

As for the Bleibtreu, I had wanted to stay in Mitte but either prices exceeded my budget or there wasn't availability for my dates. I would have preferred something with more charm and old-world style, but went instead with something that, at least from the web, looks very funky and is in what seems like a good, convenient area. Are there any concerns about the hotel or the area that I should know about?

Yes, you can stay on the S-Bahn train until Savignyplatz.
The ticket is valid to any S-Bahn station within the inner S-Bahn ring.

You can expect trains every 3-5 minutes during the day on that leg from Berlin main station to Savignyplatz.

At the main station you will arrive at subway level. Follow signs for S-Bahn (green "S" logo) all the way up to the upper/elevated platforms. Take any westbound train.

Thanks again for the information.

It's unfortunate that you pick an expensive day to stay in Berlin because normally you can get much better hotel rates in Berlin. In any case, there's nothing wrong with the Bleibtreu area, you may just get the feel of the older West Berlin built in the cold war period, but it's still a safe and quiet side street right off the old fashioned Ku'damm where many high end designer stores are located, especially west of Uhlandstrasse. You can always take the bus/train to the more vibrant and youthful East Berlin.

The farther in advance you buy tickets on bahn.de, the lower the price. I arrive in Berlin the same day as you. I've already bought most of my tickets. I leave for Dresden on 29 September and believe the cheapest fare (we paid 29eu for TWO fares back in March)is higher now. (You have to be OK with a non-refundable fare, which I was). I'd say buy now if you know where you are going and when.
I had a LOT of trouble getting the tickets printed though. Each time I bought, they failed to send me the E-ticket. Luckily, I'd noted the confirmation number and a friend in Germany got it worked out. So be careful on that end.