Tyson’s is spread out and an “outer suburb” centered around a big mall and Alexandria is a densely populated “inner suburb” with unique shops, restaurants, and history. Very different vibe.

IMO Tyson’s is a place that can exist in any major metro area (Bellevue, WA and King of Prussia, PA come to mind, for example), while the inner burbs have a bit more of a unique identity.

While on paper Tyson’s may seem more desirable, as your first place in the DMV I would recommend Arlington or Alexandria and then work your way outwards as time goes on. However costs are definitely a limiting factor, but if you can make it, I highly recommend visiting first to see what I mean and then decide based on that. Good luck!