welcome!
All are good questions, I am going to 'attempt' to answer a few of them in a general tone, since filmmaking is for each person as part of their 'life' so take it as what it is from my suggestions
First, as you said, it is to market yourself, with short is always a great idea, but if you haven't done any before, then use this opportunity to shoot many short films to learn the craft and horn your skill. If you have shorts before, then use this opportunity to market yourself by submitting to film festivals, give it freely to everyone, etc... Selling shorts are harder to do because it is a limited distribution arena. You can however, have it on atomsfilm.com or other sites where you *might* get some profit out of it... Now, before submitting like crazy to these sites that will pay, go check them out and see what sort of genre or film they show would attract a lot of viewers, these will be the ones that would dictacte how quickly you would see a 'return' to bring you back to the black (in $ perspective)
As for what to invest? it's up to you, if you are going to shoot HD or HDV, then you have to think about the post-production, if you have a venue to edit your stuff with HD or HDV, then go for it, if not, drop back to miniDV or what Shaw/Clive has suggested using the DVcPro50 format... Personally, I would recommend the dvx100 and shoot it with good lighting and sound, then color process the video to have it's own aesthetic look. It would bring out a different feel and look that might help market yourself (depending what area you want to 'sell' yourself as).
I would say, find someone who owns the camera(s) and work with them by doing some test... And decide whom to work with, these people who own the equipment might know the equipment better than you buying them and asking your friends to help you out
As for sound and lighting, they are a must, a good lighting will help make your story or your visual become reality, a good sound helps increase the production value as well, so both are not something you want to skip out of. If you can't afford to buy sound/light kit, again find people in your area that have the expertise (note, don't just hire them, make sure they have the 'experience', just a reason is that you will find a lot of people that claimed they can do this and that, but at the set, they can't do a thing, and that would drop your production value). Perhaps pay them a minimal or ask them to do it volunteering the time, since this is a short film, usually many would do it for no cost as long as you feed them.
Pre-production is the most important part of the success of your shoot and it doesn't cost you anything by planning it right

if you have everything organized ahead of time, you would have minimal disaster on your hand to deal with and also a more professional attitude for the cast/crew... Meaning, they will do a better job and help you more because they believe in your 'producing' skill. I have witnessed a lot of production here in town, many had people complaining this and that because of the director/producer didn't take their planning stage carefully and so everything is always in behind.
Remember, making a film is NOT about you, it's about the collaborative work that all the cast/crew working together to make your vision come true, if they failed to do a good job, you will get a lousy product and it's not because they don't want to, but you didn't set a good example for them to follow (there are exceptions to this rule). Particularly, these people are doing it volunteering their time, and if you tell them the shoot a project consist of 10 hours/day - 3 days shoot, they are 'expecting' a 10 hours/day - 3 days shoot, and they have to schedule things around it to accomodate you for those 3 days, hence, you might not be able to ask them to help out another day right then but have to schedule a pick-up day later the month or so... Be considerate and make sure they have plenty of drinks/food available at shoot, don't have heavy meal that after eating they'll be falling to sleep, but enough during the day they can go and munch...
I've heard of a shoot where director is asking everyone to chip in to get a pizza for lunch... *shrug* obviously many of the cast/crew on that shoot decided not to help the director anymore...
Once you spend money on the equipment (camera, lighting, sound) then you have to think about how to edit your piece (comes the computer, sound mixing, etc), and who can help you to operate these equipment... it will rack up, if you think this might be expensive route, like said earlier, find people who has the tools and work with them, learn to work in teams, this also will become a better experience to learn to collaborate. (afterall, most people who own the equipment knows how to operate them, like a DP would probably have or know of people that have lighting equipment to bring to the table, a lighting guy or a grip might know a good sound engineer to help out, etc).
In technical part my personal likeness: I like to shoot with a boom mic, I use beyerdynamic microphone, and a DIY bulb changer pole that subs for as a boom mic. I usually shoot with minidisc recorder with a mixer separately from the camera's mic but I retain the audio track from the cameras (yes I like to work with multiple cameras). The reason is simple if I don't slate or forgotten to slate, at least the camera's audio tracks can be used as a reference marker to sync up the sound recorded with my minidisc recorder.
Once the minidisc audio is layed on the stereo audio track of my NLE (in this case Premiere Pro), and a rough cut of the short is 'done', I will export several segment of the audio track and clean the audio up (so I don't have to clean a lot before hand, it can be done differently: clean it up all the audio and then sync it on post) For short film, I usually go sync it up first and then export the parts that need cleaning. I use Sony Soundforge and Noise Reduction, I downplay the background noise and tweak to make sure the audio is good. Then I lay 2 tracks of sound fx, and 2 tracks of music... Now, by working this way, I have a clean dialogue tracks, clean sound fx tracks and clean music tracks which means whenever I decided to replace the sound fx, or the music or the dialogue, it can be done very quickly.)
One thing I also do, which I wouldn't recomment... is since it is indie filmmaking, sometimes you can't get good audio, the background is gone but the dialogue suffered. In this case, I usually put a music track behind it to 'cover' the barely noticeable noise that no one would pay attention except for myself... I don't think this is good idea, but if I don't have time for ADR (bringing the actors back to do a clean dub of the dialogue), I would do that. otherwise, ADR is a must.
I am sure others will provide more info on this, but this is how I would suggest/and my basic work flow. SonnyBoo Guru has some good web video tips on editing and such, should check them out also.
Bottom line, if you plan to use this short film to showcase yourself and you don't have anyting (equipment wise), best to do is to invest in hiring good people with equipment (free or paying them a minimal) and get things rolling.
Johnny