From Lima to Cusco by Bus is aprox. 22 hours , the best bus company is CRUZ DEL SUR. www.cruzdelsur.com.pe The ticket is 38 dollars or 120 soles.
The air companies AEROCONDOR www.aerocondor.com.pe and STAR PERU www.starperu.com offer cheap tickets.
You don´t need booking to take the train to Cusco Machu Picchu, you can buy one day before to go to Macchu Picchu.
Other options to saty in Lima is Hostel Eiffel www.hostaleiffel.com and Flyingdog www.flyingdogperu.com
Both are in Miraflores neighbourhood.
March is low season in Cusco.
I spent January and February of last year making my way around Peru. If you only have 10 days travelling by bus, whilst preferable, will eat into your time, primarily because things just move at an incredibly slow pace in this part of the world. To get from Point A to Point B can take a whole day sometimes.
$199 certainly sounds like a lot to pay from Lima to Cuzco. Where did you get that quote from? I suggest checking out www.lan.com where you should be able to book a fare for about US$60-100.
Bear in mind that at Lima airport you will have a fairly long queue to wait in for Immigration when you arrive. I would say though that you should be able to make a 6am transfer. I got through Lima airport pretty quickly.
Lima isnt a bad city, although I would have to say if I was working on your timeframe I would spend just a day there and then head for the Andes. No doubt you will want to spend more time than you have in Cuzco!
Lake Titicaca, in my opinion, is definitely worth the overnight trip from Cuzco to Puno. I took a boat trip on the lake and it was so serene and quiet, I loved it. Again, everyone's tastes are different, so it really depends on what you want from your trip - Cuzco is lively and bustling with lots of ppl. Lake Titicaca is quiet and peaceful. I would try to do both if you could.
Finally, if you are spending a few days in Cuzco I HIGHLY recommend hopping on the local bus into the Sacred Valley to Pisac, Urubamba and Ollyantaytambo. The journey is spectacular! and there are some fabulous ruins to be seen on the way. Buses are reasonably regular throughout the day and run in a loop back to Cuzco. Its worth stopping off in one or other of the towns for a night. I recommend Ollyantaytambo.
Hope that helps.