First lager, yeast starter advice needed

OK, so I am going to do my first lager this weekend. A doppelbock kit.
I got some wyeast 2206XL in an activator pack and I want to use my new selfmade stirplate.

This is what I plan to do on the yeast side:

1. 36 hours before pitching I will activate the yeast pack. Should active the yeast in 6-12 hours.
2. Create 1L starter using light DME.
3. 30-24 hours before pitching transfer yeast from activator pack to starter and place on stirplate until pitching time.
4. I plan to pitch at room temp and leave it there until I see activity, then move to 50F fermentation chamber. Ferment 2-3 weeks at 50F, 3 days at room for diactyl rest, the cool to 305F and lager for weeks.

Here are my questions:
1. After activation should I place the activatr pack at roomtemp, fermentation temp (50F) ?
2. After transfering to starter should I place the stirplate at roomtemp or fermentation temp (50F) ?

I know the starter should be bigger, but I only have a 1L bottle, better small than nothing at all. Any feedback is appreciated
Hommel Homebrew

A 1 liter starter is not big enough for a Doppelbock. You need more like a gallon starter. It will still make beer, but the lag time may be significantly long and you will likely produce some noticeable off-flavors from all the yeast growth. I usually make my lager starters up to 2 weeks in advance. Between stepping them up and crash-cooling them, they can take that long.

As for the starter temperature, there are differing schools of thought on this. Some say you're only making yeast, so room temp is fine. Others say fermentation temp is best because the lager yeast can get used to fermenting warm (and produce esters, etc.) and then continue to produce some of these esters in the main ferment. I like to keep the starter ferment at or under 60°F for lagers. One general rule is that if you do ferment the starter at room temp, you should crash-cool and decant off the starter beer before pitching... otherwise the esters produced in the starter will affect the taste of your beer. Crash-cooling the starter takes longer for lager yeasts because they remain active at colder temps. 2 days of crash-cooling is usually enough.