Digital-SLR cameras vary in their max shutter speed. Entry level cameras are around 1/3000 and some might go up to 1/4000.
Higher D-SLR cameras can go as high as 1/8000.
When shooting with shutter speeds this high the lens needs to be fast. A f/1.2 lens.
A higher ISO can be used but that will also make for a noisy photo.

A Macro lens is what works best for close up photography. Depending on what brand camera you have there might be a Macro lens under $300.
There is also after market lenses such as Tamron and Sigma that great lenses that are less expensive than oem lenses.

There are several different types of memory and many brands of memory;
SD(Secure Disk) and SDHC(Secure Disk High Capacity) are the more common now.
SD will work in SDHC devices but SDHC will not work in SD only devices.
CF (Compact Flash) is now more commonly found in Digital-SLR but there are some that are SDHC.
Sony Memory Stick Duo only work in Sony. Olympus also has a xD memory for some of their cameras.
There is also a deference in speed between brands...faster is always better.
Just because a camera is a certain brand does not mean that it has to use that brand of memory, just the right type.

All of these are recording media except for High Definition which is a video resolution definition.
DvD is usually a miniDvD used in camcorders with a storage size around 2.8gig and a average record length of 20+minuets at best quality to 60 at least quality. Once the disk is finalized it cannot be recorded to again and can be played in a stand alone DvD player. Some camcorders can use miniDvD RW (rewritable).

MiniDV is a tape format for digital video. Record length is around 60 minuets in SP (standard play) to 90 minuets in LP(long play).

Hard Drive camcorders have a built in drive with storage sizes ranging anywhere from 30gig up to 160gig or higher. These camcorders have the longest record lengths.

Flash based camcorders use removable memory media with sizes ranging from 2gig up to 32gig. Record lengths vary widely. Flash Memory can be found in addition with all of the above formats but may be for photo capture only. Some camcorders are Hybrds that allow a choice of DvD or Flash..or..Hard Drive and Flash...

All these formats have their pluses and drawbacks. Some are very easy to edit with such as miniDV to needing conversion like Hard Drive and Flash.