Since battlegroup Kursk i have pretty much not player any other system but the battlegroup one, so wise choice in my eyes giving it a go. The rules play very nicely, most scenarios wont start with all units on the battlefield, they tend to trickle in as a result of rolling. However for most normal scenarios Recon units start deployed on the field, also which ever side has the most recon units will force the other player to take a chit before the battle even begins.
Chits are probably the mechanic that sets this game apart from alternatives, your army depending on how you build it will have a BR (battle rating, normally lower for German forces), each time you loose a unit, or decide to unpin units you draw a random chit from a pot, this are numbered 1-5, you add these up without telling your opponent and once your over that BR the game is lost and you withdraw. Not knowing quite how close you enemy is to being beaten adds a really nice flavor. As well as numbered chits you also get mine strikes, ammo low, air attacks and other random events you might draw. Capturing objectives also makes your enemy draw extra chits (which is where the infantry catapult can be useful).
Its worth for a fiver picking up some wooden counters from this chap
http://www.commission-figurines.co.uk/markers.html
The other difference is two types of fire, area and direct. Area simply gives you a chance to suppress an enemy unit causing a pin. Direct fire inflicts damage, but before rolling to hit you must 'spot' a target for direct fire, your soon get used to which one to use in situations as they crop up, learning when not to go for the quick kill but pin and delay has won me more games than not.
Also it is not simply I go You go, you get a certain amount of orders a turn, generally at 750 which we play
2D6 plus how many officers you have, each unit takes an order to do anything so you will have turns where you cannot move everything and have to concentrate on a certain area.
So advice on list building for overlord, my main opponent is British so should be able to give you some advice here. Your main advantage i have found with Germans in overlord is not the big cats but your infantry because of Panzerfausts. You arm up your infantry though it may be expensive with fausts and it will cause your oponent all sorts of head aches as he wont be able to just ignore your infantry as the faust is quite an anti tank weapon in the game even if its very short ranged. This brings me onto my next point which is i always think its worth taking an armored panzer grenadier squad, those half tracks are fast off road and can let you catapult you infantry quickly forward into. On the subject of infantry the German squad is split into two sections, a 3 man LMG section and a 5 man rifle section, the one problem this can occasionally present is moving about the same number of infantry to your opponent can cost more orders. However the tactical flexibility more than makes up for it, i find the three man team is great for just getting into cover with a good
LoS and sitting on overwatch while the 5 man team goes hunting objectives or tanks. The flexibility of the half track is not only the speed but you can get a good
RoF from its machinegun for laying down area or direct fire.
Infantry dealt with looking at tanks you generally cannot go far wrong with the Panzer V, the gun will punch through shermans and glass cannons like the M10 with relative ease, however if your opponent is looking to use a fair few churchills it might be worth paying the points for some of the bigger cats. The Panther is generally my favorite choice of tank, it might lack the side and rear armour of the tiger but its gun is quite a bit better and stays that way over a greater range, this is of particular use against churchill. Though against British you should always try and knock out those 17pdr armed tanks first, they will cause you major headaches left unchecked.
It is always worth upgrading one of your tanks to the Panzer Ace, the +1 to hit meaning you always hit on a 5+ is totally worth it, specially with the heavier tanks still having the power behind the guns at long range.
The one good thing i have found with tigers or even king tigers is opponents often totally over estimate the use of them and will concentrate a lot on trying to kill them, not a bad thing as the more shooting at a mobile bunker like the King Tiger is less shooting at the rest of the army, this kind of Big Cat hunting obsession can really be used to your advantage allowing you to skirt about doing more with other units.
Unlike in other games you have to think about logistics, i normally max out on logistics at anything over 750, three trucks is not much and they are easily destroyed but you will need to keep those big cats well stocked on ammo to keep them useful, also any mechanized arty for Germans pretty much needs a dedicated supply truck to work. If you have the points a first aid post is a good bump to your BR as well.
Recon wise, up to you but i always like to have at least one infantry foot patrol, i generally also have a couple of pumas while pretty weak they can make Sherman and the like think twice about rushing forward if they are positioned well, however i would imagine your opponent will be well stocked in the Recon department, the British have some nice choices specially when it comes to armoured cars. Again for any recon infantry option take the most panzerfausts you can, they are expensive for one shot weapons but just the threat value is worth the cost.
Engineering, always worth taking some sort of recovery vehicle specially with the high likely hood of having big expensive tanks in your army, the flame throwing half track is a personal favorite of mine as well, the enemy take a chit just for coming under flame attack the first time you use it and the flame thrower is a great way to deal with infantry in good cover.
Arty you have a good selection and will come down to personal taste, personally i love rocket arty but its expensive and slow reloads mean you cannot rely on it, but it hits with such a punch specially when combined with pre-registered target points (great things to take).
Specialist stuff, well always worth taking
AA, though you might have a couple of games where no planes turn up it is sods law the minute you take
AA out the list you will be faced with a game full of enemy planes. Also the Wirbelwind is awesome at engaging other targets as well, pretty much a must have item in all my German lists.
Probably need to stop typing now, but that is my advice, and that is coming from someone who likes the whole look of pumas and half-tracks etc
When your playing about with lists you should use the battlegroup builder, its a great way just to see what works and what does not.
http://battlegroupbuilder.com/
Also for rules questions or general battlegroup discussions check out the guild
http://www.guildwargamers.com/phpBB3/viewforum.php?f=303