If I run BGP on my main router and announce my IP space over two ISPs, what determines which ISP the traffic will come in on?
Simple answer: The AS-Path-length to the sender.
Complex Answers: This can be influenced. But depends on your upstreams.
Your question says: “I’ve not read enough on BGP to use it” 
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Take the time to read a good book. It’s worth the time.
Stefan
Yes it’s a learning process. I did pick up O’Reilly’s BGP book.
What’s the best technology on the mikrotiks to route outbound traffic to the shortest path on the open internet?
Pick up ‘Internet Routing Architectures’ by Bassam Halabi.
I apologize if English is not your first language, and the wording you use is because of that, rather than not understanding BGP itself, but the phrasing you use in both of your questions indicates a lack of understanding about what BGP is, and how it is just a tool that requires some significant resources, investment, and an actual problem that needs solving.
Setting up and utilizing BGP on a MikroTik, or any other router to do default-free multihoming is not an act of selecting and configuring the ‘best technology on the mikrotiks’.
A basic list of what you need to multihome on the Internet and use default-free routing with BGP is:
a) Your own ASN - for ARIN served regions, that’s a $500 initial fee, $100/year if you have no direct IP allocations from them.
To qualify, you must also prove that you are multihomed or are becoming multihomed.
b) Two or more Internet connections with providers who will give you full BGP feeds (can cost you a bit more, to a lot more).
c) A router that will hold at least two full BGP views (generally 256MB RAM minimum).
d) Globally routable address space. This either means your own address space directly from a registrar (with its significant justification prerequisites), or address space from one or both of your upstreams that is at least a full /24, that they will allow you to announce via your own ASN, through both connections, and will not filter because of their own summaries.
e) (if your upstreams require it) a published policy in a routing registry. This may cost you extra (such as radb.net).
You also probably want to have a consultant helping you out as most ISPs explicitly say that they do not provide support in setting up BGP, and frankly, the average person who knows how to set up default-free, multi-homed BGP is not cheap.
So, you need to ask yourself if this is something you need, and if so, something you are willing to pay for in time, money, and the added complexity and responsibility. It’s like deciding to become your own lawyer. If you have a specific need and are able to take on the risk, it can give you more control and flexibility. It can also expose you to a lot of headaches and liability that most people pay someone else to take responsibility for.
Thanks for the response.
The second question I asked was in regards to outbound traffic engineering. I’m wondering what’s available to route outbound traffic based on congestion and number of hops (not just ASNs).
I’m aware of the basic list of what’s needed for a BGP implementation. I have items a through d already in place.