You want to be at 10,000 & 250 coming into your destination airport.  Here's a tip I learned from Captain Mike Ray's excellent Flying the 700 Series (a good investment, as is his 757/767 book).

Go to the FIX page (hit the FIX key) and place your destination airport in there (e.g. EGLL).  Type /30 in the scratch pad and put it in RAD/DIS line.  A green circle with a radius of 30 miles will automagically appear on your HSI.  This makes it easy to monitor your descent.  I do this routinely.  I just make sure when I cross that magic circle, I am at 10,000 feet and 250 kts.  That gives me plenty of time to do whatever I have to do to have a nice landing.

As for the other issue, I can't say I have ever experienced, but I use SIDs and STARs always.  It may be that the autopilot prefers to be going in the proper general direction before engaging; I don't know.  If that is the case, simply follow ATC until you're pointed in the right direction, more or less, then hit LNAV when it says "resume own navigation."

You might consider trying out SIDs and STARs.  It is more realistic, and kind of fun to watch the autopilot follow a complex procedure.  It is more fun when you have plotted your bearings to various nav aids and are double-checking your progress, ready to take over in case of a glitch.  Also, real pilots (at least some of them) use the altitude window on the MCP to put a ceiling on their ascent, so they can never bust an altitude restriction.  Up to you.

The third-party Radar Contact canned ATC will leave you alone to follow SIDs and STARs.  It is a product well worth having for flying like this.  FSX ATC will mess you up more often than not.

As for picking a SID, there are a couple of things I do.  One is cheat.  Just go into FSX weather and set the winds coming from the direction you want to take off into.  If you want to use runway 27, set the winds at 270.  The other way is to listen to find out what the active runway is, then select your SID.  Unless things change on you, you're in good shape.  (Even then you just have to change SID's -- annoying, but probably happens in real life, too.)