There are several points to discuss:

Some BIOSes (i don't know if your Dell system is among them) are "configured" to need a Windows-partition as the first one. Actually a colleague fo mine had such a system and it took us some time to figure out what was wrong. Therefore the following might lead to an (from disk) unbootable laptop. Continue only if you have some "rescue disk" or something such. Usually there is some disk where you can recreate the factory setup, wiping out everything you wrote to the disk. If you have such a disk, TEST IT to know it works, only then continue because what i suggest you do is potentially disruptive. You test your plan B to work before even attempt to execute plan A.

In a normal case, where the above is not the case, your partition tale looks like there is a leftover from the probably factory-installed Windows. Run parted to remove all these partitions. Once the disk is completely clean reboot and start the installation of your distro. It should contain provisions for partitioning the disk.

If you need to partition by hand (or want to use the "expert mode" many installation routines offer for more control), here is a short guide to partitioning:

Start with a primary partition mounted on "/boot" as the first one of the type "ext3". It needs only 1GB (perhaps not even that much, 128MB should be sufficient), because in the installed system only the kernel image to boot and some GRUB-configuration files will be there. Even if you have several different kernel images to select from: they become hardly bigger than 1-2 MB apiece. Historically Linux could not boot from partitions located on disk cylinders 1023 and above, so out of habit i put this partition always at the very front. Because it won't change over time this is a very good place anyway. "ext3" is because Linux cannot boot from LVM-controlled logical partitions. This partition will also get the "boot" flag.

Then create a LVM partition (type "ext4") using the rest of the disk. We will do everything further within this partition.

The following "logical volumes" will be created inside the LVM partition and are not partitions in their own right. I will tell you the names (=mountpoints) and sizes and give you a short explanation for each.

<swap> size=your amount of RAM
Whenever the main memory of the system is exhausted some disk space previously set aside is used to emulate memory. This is called "swap" or "paging" space and you should see it like the jerry can of your car: it will be good to be there if you once in a while need it but do not rely on it and under no circumstance count that among the usable amount of gas you have. Your normal operation should not need any swap and if it does you do not need a bigger swap, you need more RAM.

/ size ~ 20GB
This is for your system. It is good style to separate application and system, so this will only hold the operating system, not the applications.

/altroot size ~ 20GB
I like always have a second OS installation in reserve, in case i manage to destroy one. This is for this second system. "/" and "/altroot" will reciprocally mount each other (if "/altroot" boots as "/", it will mount what is "/" normally as "/altroot") and everything else at the same place.

/home size ??
This is for your data. I'd start with as little as possible, because it is easier to grow this FS than it is to diminish it. Note that /home is for your personal data. If you have application data you should perhaps create a separate filesystem for it and use that.

Other FS you might need depend on what you want to do with your system. If you have a certain application i'd create 2 filesystems (at least) for it: one for the application binaries, its configuration and other files needed to run it. Another FS for its data. This way you can update your application while having the data unmounted and hence save from accidental manipulation.

Some general remarks: you should always try to be as flexible as possible. This means especially to give logical volumes the least possible amount of space. This way you have the most diskspace available to still distribute where necessary. If you need more you can always increase a particular FS in size.

I hope this helps.

bakunin