The only place I would recommend close to Chaguanas is Lange Park. However if you will be working at Pt. Lisas you can look into a rental at Roystonia. You can get a nice stand alone house with garden space there for 7500 TT or less.
While Lange Park is a very safe and nice neighbourhood, I would adivse you to stay away because of the traffic you can encounter on a daily basis (pricesmart/priceplaza and chaguanas main road). At times there is also flood on the endeavour roads. My adivice would be Chase Village to Couva area - always make sure that your are heading opposite to the traffic flow. Good Luck