Economic theory today differs to a very large extent from what Smith had in mind, so it would definitely not be a good start to understand current research.
Where you should start largely depends on your mathematical background and the type of topic you would like to study. Depending on the topic you have in mind, we use specific mathematical tools and it's hard to follow an argument if you don't know how people move between equations. With that being said, it is not impossible to understand without the mathematics. I'll even point you to some articles that boil things down to simple stuff and tell you where to look to see what economic theory is really like.
One thing I want to tell you before you start is how you should think about economic models. In macroeconomic theory, our models are self-contained artificial economies. In other words, once the model is solved, you can simulate events at your liking. By necessity, they are simplified versions of reality. The idea behind those models is that we're going to pick a few channels through which some things can influence human behavior. Not all of them will be there and the way we introduce those channels might be stylized, but the point is to put just enough in the model that we can talk about how much mechanisms contribute to some outcome.
This is in fact very intuitive. If you ever talked about policy with people around you, you probably have in mind mechanisms that can change how the policy will affect people. Maybe you believe some smart people will leave the country if taxes are too high, maybe you think lots of people will respond sharply to changes in governmental spending because they can't easily smooth them out by borrowing or lending at their convenience, etc. All of those probably happen at once, with some partly or even entirely offsetting others. To put relative 'weights' on these intuitive mechanisms, we make a dynamic model, put all the ingredients inside and look if the resulting model reproduces what we see in the data.
My suggestion would be to find a copy of VARIAN'S INTERMEDIATE MICROECONOMICS -- because it contains everything both with and without the mathematics. Everything readily transfers in modern macroeconomics, by the way. It has the intuitions, the graphics, the discussions and he also does the mathematics as a bonus.
All you really need, is an idea of how preferences and production lead to demand and supply functions, an idea of what an equilibrium is, and an idea of what elasticities tell you. Then, other ideas that are relevant depend on the topic you want to study.
TWO ARTICLES FOR WHEN YOU WANT TO TAKE A LOOK
Here comes an example -- a very interesting example:
This is a wonderful article by Vincenzo Quadrini about how entrepreneurship influences income distribution AND social mobility in the US. You probably will not understand sections II and III. However, you will understand the introduction, section I and section IV on results. On page 25, he shows how his model compare for wealth and income distribution with the US data. On page 26, he gives the transition matrix for his simulated model.
The gist of what he does:
1. Previous models that explicitly account for differences across people didn't feature enough factors to drive differences in wealth accumulation across people. Generally, they lead to distributions that are way less concentrated than the one seen in the data;
2. He introduces entrepeneurship. Borrowing limitations to engage in business projects and more volatile income for entrepeneurs make them likelier to save more -- which helps his model generate more inequality;
3. He talks about a stationnary distribution: this is a dynamic model, but there exists a point where the distribution of people in terms of wealth no longer changes. Individuals move across wealth classes, but the distribution is unchanged. This is the point for which he solves and simulate the model.
The reason this is so interesting is that it offers a possible explanation of inequalities. Moreover, with that kind of model, you can answer a very deep question: suppose I introduce a policy to encourage entrepreneurship, what happens? What we do is: solve the model before the policy, after the policy and, then, force a transition between both solutions. All economic models use preferences: households rank different sequences of consumption and leisure and, given the constraints they face, they pick the best feasible sequence. So, if I have a transition simulation and a no transition simulation, I can aks who would prefer the transition and who would not. All you have to do is pick any type of household in the model. Then, in the no-transition case, you find what is the constant fraction of consumption you would need to give or take away from it so that he is exactly indifferent between the transition and no-transition cases... If you do this for everyone, you have put a dynamically consistent price on the transition for every single type of household -- in other words, you can answer the question who benefits, who looses and who doesn't care.
How about we pick another topic?
That is a paper by Eggertsson on the topic of the zero lower bound. You will not understand every detail, but Eggertsson shows what happens in a simple dynamic model graphically. Basically, in modern DSGE models, if you assume central banks do nothing, you CAN consistently get extremely puzzling results. For instance, technological progress worsens the recession, tax breaks can worsen the recession, wide spread desires to save can make aggregate savings fall, wide spread desires to work more can worsen the recession.
Of course, you need specific conditions to make it work -- but I like his article because he keeps things simple and tells you how and why each curves move.