I'd be reluctant to recommend a DSO138, not just because they are "bit rubbish" (They are - I bought an eBay clone just to see what a $15 scope was about - it's a cute conversation toy but I never use it), but also because they are only 1 channel and have very limited store/review capability. In your budget you can do a LOT better.
Not knowing exactly what you intend to do, but based on "computer science student" and "digital electronics". Here's a couple of pointers that might be worth considering for a "first scope":
The more you can see at once the better. 4 channels is 10x better than 2, but 2 channels is 100x (perhaps 1000x) better than one. With a single channel you can only see one thing (obviously), but with two, you can see two signals in relation to each other - and with external trigger, you can get the relationship of three signals. Being able to walk a bus with one probe while triggering on select with the other is a HUGE advantage you just can't do with a single channel scope. In contrast, most of the things you can do with a 4 channel scope you can accomplish with a 2 channel scope if you have patience.
Being able to store and easily review a long sequence is very helpful when debugging any sort of serial bus/protocol. Your "cheap logic analyzer" will fill in a lot here, so this may not be as important, but it's still a high consideration.
These two features are the primary reason I got a DS1054Z and I think the main reason for it's popularity - 4CH and 24M samples is a LOT for the price.
Also, the physical form factor will affect you more than you think. Nothing beats having a dedicated display and dedicated knobs... you want to concentrate on your debugging, not on fiddling with your test equipment.
Next to that i would pick USB, provided that 1) I have a USB scope that actually works (most cheap ones don't), 2) I have a suitable PC already on the bench, 3) I have room on the screen and don't have to cover up other tools I need to see when using the scope and 4) I have a mouse or trackball that's not going to get in the way roaming over my work area.
My least recommendation would be for fiddly little "gadget" type tools which seem really cool, but will just annoy you when you are trying to get real work done.
If you want to go really low cost, I would second the recommendation to consider used. For some reason people tend to punt it, but I still have, use and like my TDS210 .. It's a lot more responsive than the Rigol and I'm sure you could find one under your budget. Older (bigger) very capable scopes can go for even less (assuming you have room on your bench). But like anything used, there is a certain risk aspect, and you'll be giving up a lot of the convenience of modern scopes (deeper memory, advanced functions, USB, LAN ports etc.)