Bands are mediocre at best. They are good for rehab etc... but there isn't enough INITIAL resistance, ie at the start of the movement which is arguably the most important bit as the band hasn't been stretched, and so its only the range of movement that gets truly worked where you're already strong in comparison.
Bench for example, pressing the band at the start would have no resistance, but at the top there is loads. The core component of bench is the chest, once its over half way triceps take over. Muscles evolved to be the counterpart of gravity, so using gravity as the prime resistance will yield biggest gains.
Bands won't apply enough pressure to reform bones, how say heavy squats or deadlifting would. The 3 arguable most important staples in a programme is squat, benchpress and deadlift.... elastics just can not mimic these.
You say pressups will do the same which is just not true, both mechanically and physically. A strong bench starts with strong legs, shoulders pinned back and a natural decline. You can't mimic this with bands no matter where you put them.
As for the original post, go for it. With a steady bench, a straight bar and plenty of weight there is nothing you can't achieve. Although imo for any strength or building regime squat holds priority over everything, just for the amount of growth hormone, IGF-1 and testosterone secretion directly related to the exercies which no ponsey curl or crunch will ever achieve. More test = more mass and strength, simple as that.
If money is an issue, go get a fuck off tyre and throw the cunt round the garden, failing that, rocks all the way.