You have lots of input here, but if you are concerned with wiring this sub-panel up in accordance to the NEC (National Electrical Code), you probably need some better direction than these replies (no disrespect intended to the posters, but the NEC rules can be somewhat tricky).
Here are some things to consider:
1) Do you really need this sub-panel? If you have plenty of available breaker spaces in your existing panel, the only advantage in a sub-panel is to minimize wire runs for your branch circuits.
2) What types of loads will this panel service? Will your new loads overload your main service panel's capacity? If you are only adding general use lighting and receptacle loads (even HT equipment is generally considered general use), probably not, but you mentioned HVAC. To answer these questions you will need to do a load calculation for your service, which is tricky to do. If you are so inclined, a helpful website for doing this according to the 2002 NEC can be found here: http://homewiringandmore.com/hom...DmdCalc02.html
3) You do not need a main breaker in your sub-panel if it derives power from your main service panel. Sub-panels are not service rated panels and therefore do not fall subject to a main disconnect or "6 swipe" disconnect rule. The term sub-panel implies that this is in fact a non-service rated panel, which means the sub-panel can be disconnected via the main service panel or main disconnect. If the "sub-panel" is being directly connected to a power meter, then it is not a sub-panel but a service rated panel, and many more rules apply to it's location, wire sizing, etc.
4) Are you planning on running any 240V loads, or strictly 120V?
You mentioned that you want to add (4) 20-Amp circuits and (4) 15-Amp circuits to this sub-panel. Note that if you are powering the panel with 3 current-carrying conductors (neutral and 2 wires making up the 240V), your total number of amps drawn by the panel is only HALF the sum of your total 120V loads. This is because your sub-panel will running 240V, so half the loads will be from one 120V leg, and half will be off the other (approximately). If you are certain these 8 circuits are all you will ever use from the sub-panel, you would be safe wiring the sub-panel to handle 70A, maybe even less. But if you wanted to allow for future expansion, you should wire it to handle more.
Note that wiring the sub-panel allows lots of freedom, but once you pick your wire size, you are limited in the breaker size protecting it in the main panel. If you use 8 AWG wire to the sub-panel, you cannot simply upgrade the sub-panel's capcity by upgrading the breaker in the main box from a 40A to a 50A; you would have to change the wire too.
In general, you will be better off running as large a wire as you can - better to be too big a wire than too small. Also keep in mind that certain circumstances require you to "de-rate" your wire's ampacity (temperature, number of conductors in the conduit, length of run, etc). So sizing the wire and breaker may be a little tougher than simply looking up the value in a table.
By the way, there is no hard limit to the number of receptacles you can put on a circuit. The limit is calculated based your general lighting requirement (sq footage of the finsihed area) and how many lighting branch circuits you have for that area. Local code may have a limit, however.
If you really don't want to protect yourself against having to upgrade in the future, have no dedicated loads from the sub-panel (HVAC, pumps, etc), you can get away with a 30A double-pole breaker (2 @ 30A each) and 10 AWG wire, assuming you don't have any de-rating issues.
Note that you cannot generally run NM cable against concrete basement walls and have to protect the cable's sheathing with conduit. If you keep the cable in the floor joists and in walls, you can probably run NM cable. Of course, you should check with your local inspector to be sure.
If you have to use conduit, you might want to upgrade the service to be one size bigger than needed. If you have to go through the hassle of pulling cable through conduit anyways, you might as well up-size the wire and conduit to have some room to grow!