This is a very large question, Daddy. Much depends on the time of day, what you are interested in listening and what the Sun is up to.
Let's break this down into parts - and do the easy (well, maybe not so easy) part first. HF propagation is greatly influenced by solar activity - and recently things have been a little jumpy due to several flares sending highly ionized clouds of gas in our direction. These Coronal Mass Ejections, or CMEs, are one of the mechanisms that cause the Aurora Borealis (or for our friends below the equator, the Aurora Australis).
This article from our wiki has a lot of information on the subject. I would start by viewing the excellent website AE4RV put together - note that you will need the Flash software to be active to view it. The link for this website is in the preamble of...
HF Propagation - The RadioReference Wiki
Spaceweather.com is another good website to keep handy for current conditions. Not too technical, but you also get enough detail to make you start thinking about how the sun and Earth interact.
Also keep in mind that daylight and darkness play a major role here. In general, stick above 10 Mhz during the day, below that at night.
Now to a much broader question, and one that frankly deserves a whole 'nother discussion, and that's antennas. While the height restrictions are an issue, that's not necessarily a real concern right now. A better set of questions would relate to what you want to hear, and how much area outdoors do you have to play with. We hams only occupy a very small section of the HF spectrum. We have LOTS of links on HF antennas here....
HF Antennas - The RadioReference Wiki
Learn this as you go, Daddy - when you go for your General, what you learn here will play a role later...
I should also note that we have separate forums for both these questions - propagation questions can go to the HF/MW/LW General forum, while HF listening antennas go to our Receive Antennas forum (where this thread will eventually be moved). You really have 2 (related, granted) questions here - and we'll be glad to take you through them as you learn.