+1. You really need a minimum of 3 suits to ensure proper rotation (allow the fabric to air out and wrinkles to fall out, and so on) to allow the life of the suit to... well, not be extremely short lived. You really only need a pair of black shoes for interviews and formal events, but they are a necessity at some point in the shoe wardrobe, whether first or last. You also need at least two pairs of shoes to rotate (also to air out and settle back to form), although I really think three is optimal and the minimum rotation I use.
I think the conclusion is - spend your money now on a navy or charcoal suit for your interview. Thrift it and get some alterations done. The major noticeable important alterations would be sleeve length and waist - my tailor charges $15 for sleeves and $15 for waist generally. If you have some time and patience, get your measurements taken and scour eBay, get something close to your measurements (usually slightly bigger is better, as a tailor can take away cloth, but can't add it), and have it altered. If the current shirt you have is muted, it's fine, otherwise, get a plain white dress shirt (not OCBD). The shoes you have will do for your interview. Get a tie - solid or muted pattern, dark earth tones (maroon, green, navy, etc - NOT bright red, gold, bright blue, any neon type color etc.)
I'd generalize that in the US, engineers are relatively sloppy dressers. That doesn't mean you have to be, but you need to dress at a formality level relative to your peers so as to make them comfortable. You'd look strange in a suit every day compared to your peers, managers would think you are trying to one-up them, etc, not good. I'd assume Mexico is similar. OCBDs and chinos will be perfect once you actually get the job. So, your first paycheck will be 2-3 more pairs of chinos (get maybe another shade of tan from what you already have, a navy, and maybe grey), 4-5 OCBDs (white, blue, salmon/pink, and maybe some muted stripes or gingham check), and brown shoes. Throw the black shoes in your closet and don't pull them out again until a formal event, performance assessment, another interview, etc. Again, if you have patience, you can find gold at thrift shops or eBay, but if not, do the best you can in department stores.
Fit is INFINITELY more important than quality at this stage for you. Make sure everything fits, and if it doesn't make sure you get it cheap enough to afford alterations to make it fit. The most common offenders are pant legs too long and shirts too big in the body. Get pants hemmed so the top of the pants just touches the top of your shoe and has a slight bend, should be under $10 per pair of pants to have done. If shirts are billow-y in the body or there is a lot of bunching when you tuck them in, get the shirts taken in at the sides or have darts added to slim down the body. Cost will depend on how much work is needed, but maybe anywhere from $5-15 would be a guess. It's better to have 5 perfectly fitted shirts than 10 that are huge, with the same cost in the end. You just have to do laundry more, but you'll look better every day. Some will argue to not waste money on alterations unless it's a designer piece of clothing, but you don't want to wait to look good until you can afford those brands, right?
Next purchase would be a second pair of brown shoes, different style and color. Why? Because shoes last longer when they can air out and dry out between wears, so you rotate them every day. Then, I'd sprinkle in a few more shirts and save for a third pair of brown shoes, just to expand the rotation. Pick up a second tie at some point so in the event you have to wear your suit 2 days in a row, you can at least rotate the tie (it's OK to wear the same suit 2 days in a row, no one will notice that). At that point, you don't need any more, so save your money for some life events.