Don't worry about money or high connections- there are lots of fraternities here at KSU and most all of them are very approachable.
There is really not much of a formal rush process at KSU . When I was there, we had a 4 day period where the houses were supposed to have representatives on hand from 2-6 in the afternoon to meet anyone who came by looking for more info. That was all they had.
And unless I am mistaken, even that is not done today. So the burden is pretty much completely on you to take initial steps if you want to get a good look at a large number of houses.
Roundup is coming soon and that is the first point when a lot of potential fall rushees will be coming up to check things out. From there, summer rush goes on from the end of the spring semester right up until the fall- though the real concentration of events begins in late June.
You have picked the right time to start doing your homework, and I would suggest you contact friends of yours in fraternities at KSU - or better still women you know who are in sororities and who know you well enough to give you their honest advice about where to focus your efforts. A good friend in a sorority is your best resource for starting the rush process.
Some houses will send you invitations to events- either because someone knows you or because they got a list of high school seniors and invite everybody since that school has been a good recruiting ground in the past. Don't assume that a group that sends you an unexpected invitation is a low-tier organization pushing for new members. It could just as easily be a top-tier group that has already heard good things about you.
Roundup and July 4th are two pretty significant rush periods- generally speaking. Your best bet is to talk to friends now and try to get their advice on where to focus those initial efforts since you will be best off heading into Roundup planning to rush at just a couple of places.
The majority of bids extended at most houses are given out over the summer or right at the start of the year- long before "formal rush" begins. So it is important to get moving now so that you will be all set for this summer. It varies by house, but generally speaking a serious fraternity that makes a careful selection of good potential candidates will want to see you at 3 events before a bid is extended. So you will have some serious rushing to do. Even if you come into rush with several people knowing you, a good house will not give you a bid the first time you come to a rush event.
Be careful about any situation where you get a bid the first time you meet with a fraternity. Most groups, large and small, take their time before making a decision. And it is my observation that the few groups who do give bids to everyone they can right away will tend to have very high dropout rates in pledgeship among other issues. Texas is a very expensive place to exist, which is why some groups just go for the numbers and the money- but the result is not usually what most would call a great chapter. And I will also note those chapters are where a disproportionate number of risk management tragedies take place. I will not name names, but you will figure it out as you start getting around and meeting people.
Two final pieces of advice,
1. Don't get drunk, tear up hotel rooms or do other illegal things. A lot of rushees seem to think they are expected to cut loose, but it is not true. A HUGE part of rush is making sure that potential rushees have a certain degree of discretion and social maturity.
2. When speaking with sorority women you are friends with, you can have honest conversations comparing fraternities and how their particular character may or may not make them a good home for you. But when talking to the guys where you rush, it is best to not even mention the other houses. Focus on learning about that house when you are there- and do your comparing in the company of a neutral party.